relative difference families with variable block sizes and their related oocs seven infinite classes of relative difference families with variable block sizes are presented explicitly in particular a balanced gv g k 1 df with g k k k2 k 2 is explicitly given for i k 3 4 5 and every v coprime to 6 ii k 3 4 6 3 5 6 or 3 4 5 6 and every v coprime to 30 as far as the authors are aware these difference families can be viewed as the first explicit constructions of infinite classes of optimal variable weight optical orthogonal codes with more than two weights it is observed however that there are infinitely many values of v for which an optimal v w 1 q ooc exists whatever the set of weights w and the weight distribution sequence q are

quantum field theory and hopf algebra cohomology we exhibit a hopf superalgebra structure of the algebra of field operators of quantum field theory qft with the normal product based on this we construct the operator product and the time ordered product as a twist deformation in the sense of drinfeld our approach yields formulae for perturbative products and expectation values that allow for a significant enhancement in computational efficiency as compared to traditional methods employing hopf algebra cohomology sheds new light on the structure of qft and allows the extension to interacting not necessarily perturbative qft we give a reconstruction theorem for time ordered products in the spirit of streater and wightman and recover the distinction between free and interacting theory from a property of the underlying cocycle we also demonstrate how non trivial vacua are described in our approach solving a problem in quantum chemistry

proof of the symmetry of the off diagonal hadamard seeley dewitt s coefficients in c lorentzian manifolds by a local wick rotation completing the results achieved in a previous paper we prove the symmetry of hadamard seeley dewitt off diagonal coefficients in smooth d dimensional lorentzian manifolds this result is relevant because it plays a central role in physics in particular in the theory of the stress energy tensor renormalization procedure in quantum field theory in curved spacetime to this end it is shown that in any lorentzian manifold a sort of local wick rotation of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinate are appropriate no time like killing field is necessary such a local wick rotation analytically continues the lorentzian metric in a neighborhood of any point more generally in a neighborhood of a space like cauchy hypersurface into a riemannian metric the continuation locally preserves geodesically convex neighborhoods in order to make rigorous the procedure the concept of a complex pseudo riemannian not hermitian or kahlerian manifold is introduced and some features are analyzed using these tools the symmetry of hadamard seeley dewitt off diagonal coefficients is proven in lorentzian analytical manifolds by analytical continuation of the symmetric riemannian heat kernel coefficients this continuation is performed in geodesically convex neighborhoods in common with both the metrics then the symmetry is generalized to c non analytic lorentzian manifolds by approximating lorentzian c metrics by analytic metrics in common geodesically convex neighborhoods

classical limits of unbounded quantities by strict quantization this paper extends the tools of c algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories we introduce the approach first in the simple case of finite systems then we apply this approach to analyze the classical limits of unbounded quantities in bosonic quantum field theories with particular attention to number operators and hamiltonians the methods take classical limits in a representation independent manner and so allow one to compare quantities appearing in inequivalent fock space representations

batalin vilkovisky formalism in the functional approach to classical field theory we develop the batalin vilkovisky formalism for classical field theory on generic globally hyperbolic spacetimes a crucial aspect of our treatment is the incorporation of the principle of local covariance which amounts to formulate the theory without reference to a distinguished spacetime in particular this allows a homological construction of the poisson algebra of observables in classical gravity our methods heavily rely on the differential geometry of configuration spaces of classical fields

optical orthogonal codes new bounds and an optimal construction a technique for constructing optimal oocs optical orthogonal codes is presented it provides the only known family of optimal with respect to family size oocs having lambda 2 the parameters n omega lambda are respectively p sup 2m 1 p sup m 1 2 where p is any prime and the family size is p sup m 2 three distinct upper bounds on the size of an ooc are presented that for many values of the parameter set n omega lambda improve upon the tightest previously known bound

batalin vilkovisky formalism in perturbative algebraic quantum field theory on the basis of a thorough discussion of the batalin vilkovisky formalism for classical field theory presented in our previous publication we construct in this paper the batalin vilkovisky complex in perturbatively renormalized quantum field theory the crucial technical ingredient is an extended notion of the renormalized time ordered product as a binary product equivalent to the pointwise product of classical field theory originally in causal perturbation theory the time ordered product is understood merely as a sequence of multilinear maps on the space of local functionals our extended notion of the renormalized time ordered product denoted by cdot mathcal t rm r is consistent with the old one and we found a subspace of the quantum algebra which is closed with respect to cdot mathcal t rm r on this space the renormalized batalin vilkovisky algebra is then the classical algebra but written in terms of the time ordered product together with an operator which replaces the ill defined graded laplacian of the unrenormalized theory we identify it with the anomaly term of the anomalous master ward identity of brennecke and dutsch contrary to other approaches we do not refer to the path integral formalism and do not need to use regularizations in intermediate steps

ricci flow from the renormalization of nonlinear sigma models in the framework of euclidean algebraic quantum field theory the perturbative approach to nonlinear sigma models and the associated renormalization group flow are discussed within the framework of euclidean algebraic quantum field theory and of the principle of general local covariance in particular we show in an euclidean setting how to define wick ordered powers of the underlying quantum fields and we classify the freedom in such procedure by extending to this setting a recent construction of khavkine melati and moretti for vector valued free fields as a by product of such classification we provide a mathematically rigorous proof that at first order in perturbation theory the renormalization group flow of the nonlinear sigma model is the ricci flow

on dually flat α β metrics abstract the dual flatness for riemannian metrics in information geometry has been extended to finsler metrics the aim of this paper is to study the dual flatness of the so called metrics in finsler geometry by doing some special deformations we will show that the dual flatness of an metric always arises from that of some riemannian metric in dimensional n 3

on some explicit constructions of dually flat finsler metrics abstract by using the fundamental property of the dually flat equation we manufacture explicitly new examples of dually flat finsler metrics these metrics contain the funk metric on the unit ball

on the stress energy tensor of quantum fields in curved spacetimes comparison of different regularization schemes and symmetry of the hadamard seeley dewitt coefficients we review a few rigorous and partly unpublished results on the regularisation of the stress energy in quantum field theory on curved spacetimes 1 the symmetry of the hadamard seeley dewitt coefficients in smooth riemannian a lorentzian spacetimes 2 the equivalence of the local function and the hadamard point splitting procedure in smooth static spacetimes 3 the equivalence of the dewitt schwinger and the hadamard point splitting pro cedure in smooth riemannian and lorentzian spacetimes

constructions for optimal spl upsi 4 1 optical orthogonal codes four direct constructions three of which are by way of skew starters are given in this correspondence for optimal spl upsi 4 1 optical orthogonal codes ooc s these improve the known existence results concerning optimal spl upsi 4 1 oocs in particular it is shown that an optimal spl upsi 4 1 ooc exists for all positive integers spl upsi spl equiv 6 mod 12 or spl upsi spl equiv 24 mod 48 it is also shown that an optimal 12 spl upsi 4 1 ooc exists for any positive integer spl upsi whose prime factors are all congruent to 1 modulo 4

local causal structures hadamard states and the principle of local covariance in quantum field theory in the framework of the algebraic formulation we discuss and analyse some new features of the local structure of a real scalar quantum field theory in a strongly causal spacetime in particular we use the properties of the exponential map to set up a local version of a bulk to boundary correspondence the bulk is a suitable subset of a geodesic neighbourhood of an arbitrary but fixed point p of the underlying background while the boundary is a part of the future light cone having p as its own tip in this regime we provide a novel notion for the extended algebra of wick polynomials on the aforesaid cone and on the one hand we prove that it contains the information of the bulk counterpart via an injective homomorphism while on the other hand we associate to it a distinguished state whose pull back in the bulk is of hadamard form the main advantage of this point of view arises if one uses the universal properties of the exponential map and of the light cone in order to show that for any two given backgrounds m and m and for any two subsets of geodesic neighbourhoods of two arbitrary points it is possible to engineer the above procedure such that the boundary extended algebras are related via a restriction homomorphism this allows for the pull back of boundary states in both spacetimes and thus to set up a machinery which permits the comparison of expectation values of local field observables in m and m

the generally covariant locality principle a new paradigm for local quantum field theory a new approach to the model independent description of quantum field theories will be introduced in the present work the main feature of this new approach is to incorporate in a local sense the principle of general covariance of general relativity thus giving rise to the concept of a locally covariant quantum field theory such locally covariant quantum field theories will be described mathematically in terms of covariant functors between the categories on one side of globally hyperbolic spacetimes with isometric embeddings as morphisms and on the other side of algebras with unital injective monomorphisms as morphisms moreover locally covariant quantum fields can be described in this framework as natural transformations between certain functors the usual haag kastler framework of nets of operator algebras over a fixed spacetime background manifold together with covariant automorphic actions of the isometry group of the background spacetime can be re gained from this new approach as a special case examples of this new approach are also outlined in case that a locally covariant quantum field theory obeys the time slice axiom one can naturally associate to it certain automorphic actions called relative cauchy evolutions which describe the dynamical reaction of the quantum field theory to a local change of spacetime background metrics the functional derivative of a relative cauchy evolution with respect to the spacetime metric is found to be a divergence free quantity which has as will be demonstrated in an example the significance of an energy momentum tensor up to addition of scalar functions for the locally covariant quantum field theory furthermore we discuss the functorial properties of state spaces of locally covariant quantum field theories that entail the validity of the principle of local definiteness

on a class of dually flat general α β metrics abstract in this paper we study a class of finsler metric defined by a riemannian metric a 1 form and its norm general metric we classify locally dually flat general metric when the riemannian metric is strongly dually flat and give some new examples

on some dually flat finsler metrics with orthogonal invariance abstract inspired by the integral representation of two dimensional reversible projective finsler metrics due to a v pogorelov we explicitly construct two new families of dually flat not necessarily reversible finsler metrics with orthogonal invariance of arbitrary dimension

euclidean epstein glaser renormalization in the framework of perturbative algebraic quantum field theory recently developed by brunetti dutsch and fredenhagen http arxiv org abs 0901 2038 i give a general construction of so called euclidean time ordered products i e algebraic versions of the schwinger functions for scalar quantum field theories on spaces of euclidean signature this is done by generalizing the recursive construction of time ordered products by epstein and glaser originally formulated for quantum field theories on minkowski space epstein and glaser ann inst henri poincare 19 211 1973 an essential input of epstein glaser renormalization is the causal structure of minkowski space the absence of this causal structure in the euclidean framework makes it necessary to modify the original construction of epstein and glaser at two points first the whole construction has to be performed with an only partially defined product on interaction functionals this is due to the fact that the fundamental solutions of the

construction of ym 4 with an infrared cutoff we provide the basis for a rigorous construction of the schwinger functions of the pure su 2 yang mills field theory in four dimensions in the trivial topological sector with a fixed infrared cutoff but no ultraviolet cutoff in a regularized axial gauge the construction exploits the positivity of the axial gauge at large field for small fields a different gauge more suited to perturbative computations is used this gauge and the corresponding propagator depends on large background fields of lower momenta the crucial point is to control in a non perturbative way the combined effect of the functional integrals over small field regions associated to a large background field and of the counterterms which restore the gauge invariance broken by the cutoff we prove that this combined effect is stabilizing if we use cutoffs of a certain type in momentum space we check the validity of the construction by showing that slavnov identities which express infinitesimal gauge invariance do hold non perturbatively

local wick polynomials and time ordered products of quantum fields in curved spacetime in order to have well defined rules for the perturbative calculation of quantities of interest in an interacting quantum field theory in curved spacetime it is necessary to construct wick polynomials and their time ordered products for the noninteracting theory a construction of these quantities has recently been given by brunetti fredenhagen and kohler and by brunetti and fredenhagen but they did not impose any locality or covariance condition in their constructions as a consequence their construction of time ordered products contained ambiguities involving arbitrary functions of spacetime point rather than arbitrary parameters in this paper we construct an extended wick polynomial algebra large enough to contain the wick polynomials and their time ordered products by generalizing a construction of dutsch and fredenhagen to curved spacetime we then define the notion of a local covariant quantum field and seek a definition of local wick polynomials and their time ordered products as local covariant quantum fields we introduce a new notion of the scaling behavior of a local covariant quantum field and impose scaling requirements on our local wick polynomials and their time ordered products as well as certain additional requirements such as commutation relations with the free field and appropriate continuity properties under variations of the spacetime metric for a given polynomial order in powers of the field we prove that these conditions uniquely determine the local wick polynomials and their time ordered products up to a finite number of parameters these parameters correspond to the usual renormalization ambiguities occurring in minkowski spacetime together with additional parameters corresponding to the coupling of the field to curvature we also prove existence of local wick polynomials however the issue of existence of local time ordered products is deferred to a future investigation

on generalized m th root finsler metrics in this paper we characterize locally dually flat generalized m th root finsler metrics then we find a condition under which a generalized m th root metric is projectively related to a m th root metric finally we prove that if a generalized m th root metric is conformal to a m th root metric then both of them reduce to riemannian metrics

the effective theory of strings we show that the nambu goto string and its higher dimensional generalizations can be quantized in the sense of an effective theory in any dimension of the target space the crucial point is to consider expansions around classical string configurations we are using tools from perturbative algebraic quantum field theory quantum field theory on curved spacetimes and the batalin vilkovisky formalism our model has some similarities with the luscher weisz string but we allow for arbitrary classical background string configurations and keep the diffeomorphism invariance

the time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes the time slice axiom states that the observables which can be measured within an arbitrarily small time interval suffice to predict all other observables while well known for free field theories where the validity of the time slice axiom is an immediate consequence of the field equation it was not known whether it also holds in generic interacting theories the only exception being certain superrenormalizable models in 2 dimensions in this paper we prove that the time slice axiom holds at least for scalar field theories within formal renormalized perturbation theory

spectral classification and multiplicative partitioning of constant weight sequences based on circulant matrix representation of optical orthogonal codes considering the space of constant weight sequences as the reference set for every optical orthogonal code ooc design algorithm we propose a classification method that preserves the correlation properties of sequences first we introduce the circulant matrix representation of optical orthogonal codes and based on the spectrum of circulant matrices we define the spectral classification of the set sn w of all 0 1 sequences with length n weight w and the first chip 1 then as a method for spectrally classifying the set sn w we discuss an algebraic structure called multiplicative group action using the above multiplicative group action we define an equivalence relation on sn w in order to classify it into equivalence classes called multiplicative partitions which are the same as the spectral classes the algebraic properties of the proposed partitioning such as the number of classes and the size of each class are investigated and in the case of prime n a novel formula for the number of classes is derived finally we present and prove the autocorrelation intraclass and interclass cross correlation properties of our proposed classification of the space sn w that decrease the computational complexity of search algorithms in designing and constructing n w a c ooc

combinatorial constructions of optimal optical orthogonal codes with weight 4 a v k spl lambda optical orthogonal code c is a family of 0 1 sequences of length v and weight k satisfying the following correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda for any x x sub 0 x sub 1 x sub v 1 spl isin c and any integer i spl ne 0 mod v 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda for any x x sub 0 x sub 1 x sub v 1 spl isin c y y sub 0 y sub 1 y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v a v k spl lambda optical orthogonal code ooc with spl lfloor 1 k spl lfloor v 1 k 2 spl lfloor v 2 k 2 spl lfloor spl middot spl middot spl middot spl lfloor v spl lambda k spl lambda spl rfloor m spl rfloor spl rfloor spl rfloor codewords is said to be optimal oocs are essential for success of fiber optic code division multiple access cdma communication systems the use of an optimal ooc enables the largest possible number of asynchronous users to transmit information efficiently and reliably in this paper various combinatorial constructions for optimal v 4 1 oocs such as those via skew starters and weil s theorem on character sums are given for v spl equiv 0 mod 12 these improve the known existence results on optimal oocs in particular it is shown that an optimal v 4 1 ooc exists for any positive integer v spl equiv 0 mod 24

superselection sectors and general covariance i this paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories we shall analyze sharply localizable charges and use net cohomology of j e roberts as a main tool we show that to any 4 dimensional globally hyperbolic spacetime a unique up to equivalence symmetric tensor mathrm c category with conjugates in case of finite statistics is attached to any embedding between different spacetimes the corresponding categories can be embedded contravariantly in such a way that all the charged quantum numbers of sectors are preserved this entails that to any spacetime is associated a unique gauge group up to isomorphisms and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups this form of covariance between sectors also brings to light the issue whether local and global sectors are the same we conjecture this holds that at least on simply connected spacetimes it is argued that the possible failure might be related to the presence of topological charges our analysis seems to describe theories which have a well defined short distance asymptotic behaviour

existence of local covariant time ordered products of quantum fields in curved spacetime we establish the existence of local covariant time ordered products of local wick polynomials for a free scalar field in curved spacetime our time ordered products satisfy all of the hypotheses of our previous uniqueness theorem so our construction essentially completes the analysis of the existence uniqueness and renormalizability of the perturbative expansion for nonlinear quantum field theories in curved spacetime as a byproduct of our analysis we derive a scaling expansion of the time ordered products about the total diagonal that expresses them as a sum of products of polynomials in the curvature times lorentz invariant distributions plus a remainder term of arbitrarily low scaling degree

existence theorem for gauge algebra a general gauge action is defined by postulating a minimum of its properties necessary for the existence of loop expansion in the quantum theory the structure of the general gauge algebra is derived from these postulates the proof of existence of the structure functions lacking in previous works is given the question of uniqueness is also completely cleared up some unsolved problems are discussed in connection with the covariant quantization conjecture

algebraic quantum field theory perturbation theory and the loop expansion the perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory we show that the algebra of interacting fields is additive i e fully determined by its subalgebras associated to arbitrary small subregions of minkowski space we also give an algebraic formulation of the loop expansion by introducing a projective system n of observables up to n loops where 0 is the poisson algebra of the classical field theory finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of green s functions

optimal 2 d n times m 3 2 1 optical orthogonal codes optical orthogonal codes are commonly used as signature codes for optical code division multiple access systems so far research on 2 d optical orthogonal codes has mainly concentrated on the same autocorrelation and cross correlation constraints in this paper we are concerned about optimal 2 d optical orthogonal codes with the autocorrelation a and the cross correlation 1 some combinatorial constructions for 2 d n m k a 1 optical orthogonal codes are presented when k 3 and a 2 the exact number of codewords of an optimal 2 d n m 3 2 1 optical orthogonal code is determined for any positive integers n 0 1 3 6 9 10 mod 12 and m 2 mod 4

bounds and constructions of optimal n 4 2 1 optical orthogonal codes in this paper a tight upper bound on the maximum possible code size of n 4 2 1 oocs and some direct and recursive constructions of optimal n 4 2 1 oocs attaining the upper bound are give

conformal generally covariant quantum field theory the scalar field and its wick products in this paper we generalize the construction of generally covariant quantum theories given in bfv03 to encompass the conformal covariant case after introducing the abstract framework we discuss the massless conformally coupled klein gordon field theory showing that its quantization corresponds to a functor between two certain categories at the abstract level the ordinary fields could be thought of as natural transformations in the sense of category theory we show that the wick monomials without derivatives wick powers can be interpreted as fields in this generalized sense provided a non trivial choice of the renormalization constants is given a careful analysis shows that the transformation law of wick powers is characterized by a weight and it turns out that the sum of fields with different weights breaks the conformal covariance at this point there is a difference between the previously given picture due to the presence of a bigger group of covariance it is furthermore shown that the construction does not depend upon the scale appearing in the hadamard parametrix used to regularize the fields finally we briefly discuss some further examples of more involved fields

optical orthogonal codes design analysis and applications an optical orthogonal code ooc is a family of 0 1 sequences with good auto and cross correlation properties i e the autocorrelation of each sequence exhibits the thumbtack shape and the cross correlation between any two sequences remains low throughout the use of optical orthogonal codes enables a large number of asynchronous users to transmit information efficiently and reliably the thumbtack shaped autocorrelation facilitates the detection of the desired signal and low profile cross correlation reduces interference from unwanted signals theoretical upper and lower bounds on the maximum possible size of oocs are derived methods for the design and analysis of oocs using tools from projective geometry the greedy algorithm iterative constructions algebraic coding theory block design and various other combinational disciplines are discussed

anomalies in time ordered products and applications to the bv brst formulation of quantum gauge theories we show that every graded derivation on the algebra of free quantum fields and their wick powers in curved spacetimes gives rise to a set of anomalous ward identities for time ordered products with an explicit formula for their classical limit we study these identities for the koszul tate and the full brst differential in the bv brst formulation of perturbatively interacting quantum gauge theories and clarify the relation to previous results in particular we show that the quantum brst differential the quantum antibracket and the higher order anomalies form an l infty algebra the defining relations of this algebra ensure that the gauge structure is well defined on cohomology classes of the quantum brst operator i e observables furthermore we show that one can determine contact terms such that also the interacting time ordered products of multiple interacting fields are well defined on cohomology classes an important technical improvement over previous treatments is the fact that all our relations hold off shell and are independent of the concrete form of the lagrangian including the case of open gauge algebras

projectively flat finsler metrics of constant flag curvature finsler metrics on an open subset in r n with straight geodesics are said to be projective it is known that the flag curvature of any projective finsler metric is a scalar function of tangent vectors the flag curvature must be a constant if it is riemannian in this paper we discuss the classification problem on projective finsler metrics of constant flag curvature we express them by a taylor expansion or an algebraic formula many examples constructed in this paper can be used as models in finsler geometry

dimensional regularization in position space and a forest formula for epstein glaser renormalization we reformulate dimensional regularization as a regularization method in position space and show that it can be used to give a closed expression for the renormalized time ordered products as solutions to the induction scheme of epstein glaser this closed expression which we call the epstein glaser forest formula is analogous to zimmermann s forest formula for bph renormalization for scalar fields the resulting renormalization method is always applicable we compute several examples we also analyze the hopf algebraic aspects of the combinatorics our starting point is the main theorem of renormalization of stora and popineau and the arising renormalization group as originally defined by stuckelberg and petermann

supergeometry in locally covariant quantum field theory in this paper we analyze supergeometric locally covariant quantum field theories we develop suitable categories sloc of super cartan supermanifolds which generalize lorentz manifolds in ordinary quantum field theory and show that starting from a few representation theoretic and geometric data one can construct a functor mathfrak a sloc to s alg to the category of super algebras which can be interpreted as a non interacting super quantum field theory this construction turns out to disregard supersymmetry transformations as the morphism sets in the above categories are too small we then solve this problem by using techniques from enriched category theory which allows us to replace the morphism sets by suitable morphism supersets that contain supersymmetry transformations as their higher superpoints we construct super quantum field theories in terms of enriched functors mathfrak e mathfrak a esloc to es alg between the enriched categories and show that supersymmetry transformations are appropriately described within the enriched framework as examples we analyze the superparticle in 1 1 dimensions and the free wess zumino model in 3 2 dimensions

on the renormalization group in curved spacetime we define the renormalization group flow for a renormalizable interacting quantum field in curved spacetime via its behavior under scaling of the spacetime metric g 2g we consider explicitly the case of a scalar field with a self interaction of the form 4 although our results should generalize straightforwardly to other renormalizable theories we construct the interacting field as well as its wick powers and their time ordered products as formal power series in the algebra generated by the wick powers and time ordered products of the free field and we determine the changes in the interacting field observables resulting from changes in the renormalization prescription our main result is the proof that for any fixed renormalization prescription the interacting field algebra for the spacetime m 2g with coupling parameters p is isomorphic to the interacting field algebra for the spacetime m g but with different values p of the coupling parameters the map p p yields the renormalization group flow the notion of essential and inessential coupling parameters is defined and we define the notion of a fixed point as a point p in the parameter space for which there is no change in essential parameters under renormalization group flow

optical orthogonal codes their bounds and new optimal constructions a v k spl lambda sub a spl lambda sub c optical orthogonal code ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two correlation properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les spl lambda sub a for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c and any integer i not equivalent 0 mod v and 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les spl lambda sub b for any x x sub 0 x sub 1 spl middot spl middot spl middot x sub v 1 spl isin c y y sub 0 y sub 1 spl middot spl middot spl middot y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are taken modulo v the study of optical orthogonal codes is motivated by an application in optical code division multiple access communication systems in this paper upper bounds on the size of an optical orthogonal code are discussed several new constructions for optimal optical orthogonal codes with weight k spl ges 4 and correlation constraints spl lambda sub a spl lambda sub c 1 are described by means of optimal cyclic packings many new infinite series of such optimal optical orthogonal codes are thus produced

analytic dependence is an unnecessary requirement in renormalization of locally covariant qft finite renormalization freedom in locally covariant quantum field theories on curved spacetime is known to be tightly constrained under certain standard hypotheses to the same terms as in flat spacetime up to finitely many curvature dependent terms these hypotheses include in particular locality covariance scaling microlocal regularity and continuous and analytic dependence on the metric and coupling parameters the analytic dependence hypothesis is somewhat unnatural because it requires that locally covariant observables which are simultaneously defined on all spacetimes depend continuously on an arbitrary metric with the dependence strengthened to analytic on analytic metrics moreover the fact that analytic metrics are globally rigid makes the implementation of this requirement at the level of local algebras of observables rather technically cumbersome we show that the conditions of locality covariance scaling and a naturally strengthened microlocal spectral condition are actually sufficient to constrain the allowed finite renormalizations equally strongly thus eliminating both the continuity and the somewhat unnatural analyticity hypotheses the key step in the proof uses the peetre slovak theorem on the characterization of in general non linear differential operators by their locality and regularity properties

the master ward identity and generalized schwinger dyson equation in classical field theory in the framework of perturbative quantum field theory a new universal renormalization condition called master ward identity was recently proposed by one of us m d in a joint paper with f m boas the main aim of the present paper is to get a better understanding of the master ward identity by analyzing its meaning in classical field theory it turns out that it is the most general identity for classical local fields which follows from the field equations it is equivalent to a generalization of the schwinger dyson equation and is closely related to the quantum action principle of lowenstein and lam as a byproduct we give a self contained treatment of peierls manifestly covariant definition of the poisson bracket

functional properties of hormander s space of distributions having a specified wavefront set the space mathcal d gamma prime of distributions having their wavefront sets in a closed cone gamma has become important in physics because of its role in the formulation of quantum field theory in curved spacetime in this paper the topological and bornological properties of mathcal d gamma prime and its dual mathcal e lambda prime are investigated it is found that mathcal d gamma prime is a nuclear semi reflexive and semi montel complete normal space of distributions its strong dual mathcal e lambda prime is a nuclear barrelled and ultra bornological normal space of distributions which however is not even sequentially complete concrete rules are given to determine whether a distribution belongs to mathcal d gamma prime whether a sequence converges in mathcal d gamma prime and whether a set of distributions is bounded in mathcal d gamma prime

micro local approach to the hadamard condition in quantum field theory on curved space time for the two point distribution of a quasi free klein gordon neutral scalar quantum field on an arbitrary four dimensional globally hyperbolic curved space time we prove the equivalence of 1 the global hadamard condition 2 the property that the feynman propagator is a distinguished parametrix in the sense of duistermaat and hormander and 3 a new property referred to as the wave front set spectral condition wfssc because it is reminiscent of the spectral condition in axiomatic quantum field theory on minkowski space results in micro local analysis such as the propagation of singularities theorem and the uniqueness up toc of distinguished parametrices are employed in the proof we include a review of kay and wald s rigorous definition of the global hadamard condition and the theory of distinguished parametrices specializing to the case of the klein gordon operator on a globally hyperbolic space time as an alternative to a recent computation of the wave front set of a globally hadamard two point distribution on a globally hyperbolic curved space time given elsewhere by kohler to correct an incomplete computation in 32 we present a version of this computation that does not use a deformation argument such as that used in fulling narcowich and wald and is independent of the cauchy evolution argument of fulling sweeny and wald both of which are relied upon in kohler s proof this leads to a simple micro local proof of the preservation of hadamard form under cauchy evolution first shown by fulling sweeny and wald relying only on the propagation of singularities theorem in another paper 33 the equivalence theorem is used to prove a conjecture by kay that a locally hadamard quasi free klein gordon state on any globally hyperbolic curved space time must be globally hadamard

the epstein glaser approach to perturbative quantum field theory graphs and hopf algebras the paper aims at investigating perturbative quantum field theory in the approach of epstein and glaser eg and in particular its formulation in the language of graphs and hopf algebras has various has are encountered each one associated with a special combination of physical concepts such as normalization localization pseudounitarity causal regularization and renormalization the algebraic structures representing the perturbative expansion of the s matrix are imposed on operator valued distributions equipped with appropriate graph indices translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras the algebraic results are given embedded in the corresponding physical framework covering the two eg versions by fredenhagen and scharf that differ with respect to the concrete recursive implementation of causality besides the ultraviolet divergences occurring in feynman s representation are mathematically reasoned as a final result the change of the renormalization scheme in the context of eg is modeled via a ha and interpreted as the eg analog of kreimer s ha the paper aims at investigating perturbative quantum field theory in the approach of epstein and glaser eg and in particular its formulation in the language of graphs and hopf algebras has various has are encountered each one associated with a special combination of physical concepts such as normalization localization pseudounitarity causal regularization and renormalization the algebraic structures representing the perturbative expansion of the s matrix are imposed on operator valued distributions equipped with appropriate graph indices translation invariance ensures the algebras to be analytically well defined and graded total symmetry allows to formulate bialgebras the algebraic results are given embedded in the corresponding physical framework covering the two eg versions by fredenhagen and scharf that differ with respect to the concrete recursive implementation of causality besides the ultraviolet divergences occurring in feynman s representation are mathematically reasoned as a

equivalence of the generalised hadamard and microlocal spectrum condition for generalised free fields in curved spacetime we prove that the singularity structure of all n point distributions of a state of a generalised real free scalar field in curved spacetime can be estimated if the two point distribution is of hadamard form in particular this applies to the free field and the result has applications in perturbative quantum field theory showing that the class of all hadamard states is the state space of interest in our proof we assume that the field is a generalised free field i e that it satisfies scalar c number commutation relations but it need not satisfy an equation of motion the same arguments also work for anti commutation relations and for vector valued fields to indicate the strengths and limitations of our assumption we also prove the analogues of a theorem by borchers and zimmermann on the self adjointness of field operators and of a weak form of the jost schroer theorem the original proofs of these results make use of analytic continuation arguments in our case no analyticity is assumed but to some extent the scalar commutation relations can take its place

a new recursive construction for optical orthogonal codes we present a new recursive construction for n spl omega spl lambda sub a spl lambda sub c optical orthogonal codes for the case of spl lambda sub a spl lambda sub c spl lambda this recursive construction enlarges the original family with spl lambda unchanged and produces a new family of asymptotically optimal codes if the original family is asymptotically optimal we call a code asymptotically optimal following the definition of o moreno et al see ibid vol 41 p 448 55 1995 if as n the length of code goes to infinity the ratio of the number of codewords to the corresponding johnson bound approaches unity

essential self adjointness of wick squares in quasi free hadamard representations on curved spacetimes we investigate whether a symmetric second order wick polynomial t of a free scalar field including derivatives is essentially self adjoint on the natural wightman domain in a quasi free i e fock space hadamard representation our results apply to arbitrary spacetime dimensions d 2 but we do restrict our attention to the case where t is smeared with a test function from a particular class s namely the class of sums of squares of test functions this class of smearing functions is smaller than the class of all non negative test functions a fact which follows hilbert s theorem combining techniques from microlocal and functional analysis we prove that t is essentially self adjoint if it is a wick square without derivatives in the presence of derivatives we prove the weaker result that t is essentially self adjoint if its compression to the one particle hilbert space is essentially self adjoint for the latter result we use wust s theorem and an application of konrady s trick in fock spac

on the issue of imposing boundary conditions on quantum fields an interesting example of the deep interrelation between physics and mathematics is obtained when trying to impose mathematical boundary conditions on physical quantum fields this procedure has recently been re examined with care comments on that and previous analysis are provided here together with considerations on the results of the purely mathematical zeta function method in an attempt at clarifying the issue hadamard regularization is invoked in order to fill the gap between the infinities appearing in the qft renormalized results and the finite values obtained in the literature with other procedures

microlocal analysis and interacting quantum field theories renormalization on physical backgrounds we present a perturbative construction of interacting quantum field theories on smooth globally hyperbolic curved space times we develop a purely local version of the stuckelberg bogoliubov epstein glaser method of renormalization by using techniques from microlocal analysis relying on recent results of radzikowski kohler and the authors about a formulation of a local spectrum condition in terms of wave front sets of correlation functions of quantum fields on curved space times we construct time ordered operator valued products of wick polynomials of free fields they serve as building blocks for a local perturbative definition of interacting fields renormalization in this framework amounts to extensions of expectation values of time ordered products to all points of space time the extensions are classified according to a microlocal generalization of steinmann scaling degree corresponding to the degree of divergence in other renormalization schemes as a result we prove that the usual perturbative classification of interacting quantum field theories holds also on curved space times finite renormalizations are deferred to a subsequent paper as byproducts we describe a perturbative construction of local algebras of observables present a new definition of wick polynomials as operator valued distributions on a natural domain and we find a general method for the extension of distributions which were defined on the complement of some surface

supersymmetric field theoretic models on a supermanifold we propose the extension of some structural aspects that have successfully been applied in the development of the theory of quantum fields propagating on a general space time manifold so as to include superfield models on a supermanifold we only deal with the limited class of supermanifolds which admit the existence of a smooth body manifold structure our considerations are based on the catenacci reina teofillatto bryant approach to supermanifolds in particular we show that the class of supermanifolds constructed by bonora pasti tonin satisfies the criteria which guarantee that a supermanifold admits a hausdorff body manifold this construction is the closest to the physicist s intuitive view of superspace as a manifold with some anticommuting coordinates where the odd sector is topologically trivial the paper also contains a new construction of superdistributions and useful results on the wavefront set of such objects moreover a generalization of the spectral condition is formulated using the notion of the wavefront set of superdistributions which is equivalent to the requirement that all of the component fields satisfy on the body manifold a microlocal spectral condition proposed by brunetti fredenhagen kohler

a new class of optimal optical orthogonal codes with weight five a v k 1 optical orthogonal code ooc or briefly a v k 1 ooc c is a family of 0 1 sequences of length v and weight k satisfying the following two properties 1 spl sigma sub 0 spl les t spl les v 1 x sub t x sub t i spl les 1 for any x x sub 0 x sub 1 x sub v 1 spl isin c and any integer i spl ne 0 mod v 2 spl sigma sub 0 spl les t spl les v 1 x sub t y sub t i spl les 1 for any x x sub 0 x sub 1 x sub v 1 spl isin c y y sub 0 y sub 1 y sub v 1 spl isin c with x spl ne y and any integer i where the subscripts are reduced modulo v a v k 1 ooc is optimal if it contains spl lfloor v 1 k k 1 spl rfloor codewords in this note we establish that there exists an optimal 3 sup s 5v 5 1 ooc for any nonnegative integer s whenever visa product of primes congruent to 1 modulo 4 this improves the known existence results concerning optimal oocs

quantum energy inequalities and local covariance i globally hyperbolic spacetimes we begin a systematic study of quantum energy inequalities qeis in relation to local covariance we define notions of locally covariant qeis of both absolute and difference types and show that existing qeis satisfy these conditions local covariance permits us to place constraints on the renormalized stress energy tensor in one spacetime using qeis derived in another in subregions where the two spacetimes are isometric this is of particular utility where one of the two spacetimes exhibits a high degree of symmetry and the qeis are available in simple closed form various general applications are presented including a priori constraints depending only on geometric quantities on the ground state energy density in a static spacetime containing locally minkowskian regions in addition we present a number of concrete calculations in both two and four dimensions that demonstrate the consistency of our bounds with various known ground and thermal state energy densities examples considered include the rindler and misner spacetimes and spacetimes with toroidal spatial sections in this paper we confine the discussion to globally hyperbolic spacetimes subsequent papers will also discuss spacetimes with boundary and other related issues

renormalization proof for massive phi_4 4 theory on riemannian manifolds in this paper we present an inductive renormalizability proof for massive phi 4 4 theory on riemannian manifolds based on the wegner wilson flow equations of the wilson renormalization group adapted to perturbation theory the proof goes in hand with bounds on the perturbative schwinger functions which imply tree decay between their position arguments an essential prerequisite is precise bounds on the short and long distance behaviour of the heat kernel on the manifold with the aid of a regularity assumption often taken for granted we also show that for suitable renormalization conditions the bare action takes the minimal form that is to say there appear the same counterterms as in flat space apart from a logarithmically divergent one which is proportional to the scalar curvature

wavefront sets in algebraic quantum field theory the investigation of wavefront sets of n point distributions in quantum field theory has recently acquired some attention stimulated by results obtained with the help of concepts from microlocal analysis in quantum field theory in curved spacetime in the present paper the notion of wavefront set of a distribution is generalized so as to be applicable to states and linear functionals on nets of operator algebras carrying a covariant action of the translation group in arbitrary dimension in the case where one is given a quantum field theory in the operator algebraic framework this generalized notion of wavefront set called asymptotic correlation spectrum is further investigated and several of its properties for physical states are derived we also investigate the connection between the asymptotic correlation spectrum of a physical state and the wavefront sets of the corresponding wightman distributions if there is a wightman field affiliated to the local operator algebras finally we present a new result generalizing known facts which shows that certain spacetime points must be contained in the singular supports of the 2n point distributions of a non trivial wightman field

the microlocal spectrum condition and wick polynomials of free fields on curved spacetimes quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis we discuss a condition on the wave front set for the correspondingn point distributions called microlocal spectrum condition sc on minkowski space this condition is satisfied as a consequence of the usual spectrum condition based on radzikowski s determination of the wave front set of the two point function of a free scalar field satisfying the hadamard condition in the kay and wald sense we construct in the second part of this paper all wick polynomials including the energy momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition

the microlocal spectrum condition initial value formulations and background independence we analyze implications of the microlocal spectrum hadamard condition for states in a linear quantum field theory on a globally hyperbolic spacetime m in the context of a distributional initial value formulation more specifically we work in 3 1 split m and give a bound independent of the spacetime metric on the wave front sets of the initial data for a quasi free hadamard state in a quantum field theory defined by a normally hyperbolic differential operator p acting in a vector bundle e m this aims at a possible way to apply the concept of hadamard states within approaches to quantum field theory gravity relying on a hamiltonian formulation potentially without a classical background metric g