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

homotopy perturbation method for quadratic riccati differential equation and comparison with adomian s decomposition method abstract in this paper a homotopy perturbation method is proposed to solve quadratic riccati differential equation comparisons are made between adomian s decomposition method adm and the exact solution and the proposed method the results reveal that the proposed method is very effective and simple

sextic b spline collocation method for solving euler bernoulli beam models a numerical method based on sextic b spline is developed to solve the fourth order time dependent partial differential equations subjected to fixed and cantilever boundary conditions we use finite difference approximation to discretize the temporal variable and the spatial variable by means of a s method email protected 0 1 s 12 corresponds to the crank nicolson method and a sextic b spline collocation method on uniform meshes respectively using von neumann method the proposed method is also shown to be conditionally stable if s 0 25 the convergence analysis of the proposed sextic b spline approximation for the euler bernoulli problem is discussed in details and we have shown under appropriate conditions the proposed method converges some physical examples and their numerical results are provided to justify the advantages of the proposed method

algebraic supersymmetry a case study the treatment of supersymmetry is known to cause difficulties in the c algebraic framework of relativistic quantum field theory several no go theorems indicate that super derivations and super kms functionals must be quite singular objects in a c algebraic setting in order to clarify the situation a simple supersymmetric chiral field theory of a free fermi and bose field defined on mathbb r is analyzed it is shown that a meaningful c version of this model can be based on the tensor product of a car algebra and a novel version of a ccr algebra the resolvent algebra the elements of this resolvent algebra serve as mollifiers for the super derivation within this model unbounded yet locally bounded graded kms functionals are constructed and proven to be supersymmetric from these kms functionals chern characters are obtained by generalizing formulae of kastler and of jaffe lesniewski and osterwalder the characters are used to define cyclic cocycles in the sense of connes noncommutative geometry which are locally entire

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

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

solving riccati differential equation using adomian s decomposition method in this paper we suggest a method to solve the matrix riccati differential equation the suggested method which we called multistage adomian s decomposition method madm can be considered as an extension of the adomian s decomposition method adm which is very efficient in solving a variety of differential and algebraic equations the solution is introduced in a recursive form which can be used to obtain the solution for the whole time horizon comparisons are made between madm and the exact solution and further between madm and different numerical methods

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

wavefront sets and polarizations on supermanifolds in this paper we develop the foundations for microlocal analysis on supermanifolds making use of pseudodifferential operators on supermanifolds as introduced by rempel and schmitt we define a suitable notion of super wavefront set for superdistributions which generalizes dencker s polarization sets for vector valued distributions to supergeometry in particular our super wavefront sets detect polarization information of the singularities of superdistributions we prove a refined pullback theorem for superdistributions along supermanifold morphisms which as a special case establishes criteria when two superdistributions may be multiplied as an application of our framework we study the singularities of distributional solutions of a supersymmetric field theory

dual reciprocity bem applied to transient elastodynamic problems with differential quadrature method in time this paper is concerned with numerical analysis of the transient elastodynamic problems by the dual reciprocity bem drbem in space combined with the differential quadrature method dqm in time emphasis is placed on a comparative study of various time marching schemes three numerical examples considered are for the longitudinal forced vibration of plates and the transverse free vibration of membranes to authors best knowledge this is the first attempt to apply the dqm to the second order time derivative in the drbem elastodynamic formulations a recent approach using boundary conditions in the dqm was here extended to handle the initial conditions of elastodynamic problems the resulting algebraic formulation is a lyapunov matrix equation which can be very efficiently solved by the bartels stewart algorithm it is revealed that the dqm is an unconditionally stable algorithm and gives much better accuracy than the standard finite difference schemes such as the wilson newmark and houbolt methods for the same time step size for the cases considered

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

jacobi collocation method for the approximate solution of some fractional order riccati differential equations with variable coefficients abstract this paper presents a computational method for the approximate solution of arbitrary order non linear fractional riccati differential equations with variable coefficients proposed computational method is a combination of the operational matrix of integration method and the collocation method associated with the jacobi polynomials convergence analysis of the proposed method is provided numerical results for different fractional orders of the riccati differential equations are discussed figures and tables are used to show the numerical results derived from the proposed computational method for particular cases of jacobi polynomials such as the legendre polynomials the chebyshev polynomials of the second kind the chebyshev polynomials of the third kind the chebyshev polynomial of the fourth kind and the gegenbauer or ultraspherical polynomials numerical results from the proposed methods are compared from those derived by using the existing analytical and numerical methods it is observed that the results from the proposed method are more accurate maximum absolute error and the root mean square error tables are given for all five kinds of polynomials for comparison purposes

a new method for determining the solution of riccati differential equations abstract this paper presents a new and efficient approach for determining the solution of riccati differential equation the riccati equation is first converted to a second order linear ordinary differential equation and then to a volterra integral equation by solving the resulting volterra equation by means of taylor s expansion the approximate solution of riccati differential equation is obtained which can be achieved by symbolic computation the accuracy of approximate solution can be further improved with the increase of the order of approximations an error analysis is given test examples demonstrate the effectiveness of the method a comparison between the present results with previous results is made inferring that the suggested method is not only enough accurate but also quite stable

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

a differential quadrature based procedure for parameter identification in this paper a numerical scheme for a parameter identification problem is presented the problem here considered is the identification of the stiffness of structural elements and a new procedure to solve it is proposed this procedure involves not only the usual newton like iterative algorithm for nonlinear least squares problems but it also provides a unitary framework to calculate the solution of the equation of motion forward problem and the jacobian matrix required by minimization by means of differential quadrature dq rules simultaneously applied in space and time dq based methods are promising numerical schemes and a novel application is here proposed two practical example applications are discussed the proposed method is very simple in its principle and has great potential for future applications provided that a suitable model is adopted

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

iterative reproducing kernel hilbert spaces method for riccati differential equations this paper presents iterative reproducing kernel hilbert spaces method irkhsm to obtain the numerical solutions for riccati differential equations with constant and variable coefficients representation of the exact solution is given in the w 2 2 0 x reproducing kernel space numerical solution of riccati differential equations is acquired by interrupting the n term of the exact solution also the error of the numerical solution is monotone decreasing in terms of the norm of w 2 2 0 x the outcomes from numerical examples show that the present iterative algorithm is very effective and convenient

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

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

a generalization of the idq method and a dq based approach to approximate non smooth solutions in structural analysis abstract in this paper a new differential quadrature dq based approach in deducing the discretized equations governing the static and the dynamic problem of the euler bernoulli beam is proposed these equations here called generalized can be written easily also thanks to a lemma introduced for the first time which allow a compact writing of the solution by means of a careful distribution of the sampling points the proposed method overcomes the drawback of the element subdivision where load conditions change this is particularly useful in the analysis of some multi degree of freedom dynamic systems as it will be shown the cited distribution and the way of generating it allow to generalize the iterative differential quadrature method confined in its initial form to the two degree of freedom systems