locality in gns representations of deformation quantization in the framework of deformation quantization we apply the formal gns construction to find representations of the deformed algebras in pre hilbert spaces over and establish the notion of local operators in these pre hilbert spaces the commutant within the local operators is used to distinguish thermal from pure representations the computation of the local commutant is xemplified in various situations leading to the physically reasonable distinction between thermal representations and pure ones moreover an analogue of von neumann s double commutant theorem is proved in the particular situation of a gns representation with respect to a kms functional and for the schrodinger representation on cotangent bundles finally we prove a formal version of the tomita takesaki theorem

a continuous field of c algebras and the tangent groupoid for manifolds with boundary abstract for a smooth manifold x with boundary we construct a semi groupoid t x and a continuous field c r t x of c algebras which extend connes construction of the tangent groupoid we show the asymptotic multiplicativity of scaled truncated pseudodifferential operators with smoothing symbols and compute the k theory of the associated symbol algebra

the atiyah bott patodi method in deformation quantization we give a new proof of the index theorem for deformation quantization following the atiyah bott patodi scheme the main ingredient consists of tamarkin s theorem on topological invariants of symplectic connections which is a symplectic analog of the well known theorems for riemannian connections

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

on the set of imputations induced by the k additive core an extension to the classical notion of core is the notion of k additive core that is the set of k additive games which dominate a given game where a k additive game has its mobius transform or harsanyi dividends vanishing for subsets of more than k elements therefore the 1 additive core coincides with the classical core the advantages of the k additive core is that it is never empty once k geq 2 and that it preserves the idea of coalitional rationality however it produces k imputations that is imputations on individuals and coalitions of at most k individuals instead of a classical imputation therefore one needs to derive a classical imputation from a k order imputation by a so called sharing rule the paper investigates what set of imputations the k additive core can produce from a given sharing rule

a formal model of berezin toeplitz quantization we give a new construction of symbols of the differential operators on the sections of a quantum line bundle l over a kahler manifold m using the natural contravariant connection on l these symbols are the functions on the tangent bundle tm polynomial on fibres for high tensor powers of l the asymptotics of the composition of these symbols leads to the star product of a deformation quantization with separation of variables on tm corresponding to some pseudo kahler structure on tm surprisingly this star product is intimately related to the formal symplectic groupoid with separation of variables over m we extend the star product on tm to generalized functions supported on the zero section of tm the resulting algebra of generalized functions contains an idempotent element which can be thought of as a natural counterpart of the bergman projection operator using this idempotent we define an algebra of toeplitz elements and show that it is naturally isomorphic to the algebra of berezin toeplitz deformation quantization on m

the generalized forward backward method for analyzing the scattering from targets on ocean like rough surfaces in holliday et al 1995 1996 the iterative forward backward fb method has been proposed to solve the magnetic field integral equation mfie for smooth one dimensional 1 d rough surfaces this method has proved to be very efficient converging in a very small number of iterations nevertheless this solution becomes unstable when some obstacle like a ship or a large breaking wave is included in the original problem in this paper we propose a new method the generalized forward backward gfb method to solve such kinds of complex problems the approach is formulated for the electric field integral equation efie which is solved using a hybrid combination of the conventional fb method and the method of moments mom the latter of which is only applied over a small region around the obstacle the gfb method is shown to provide accurate results while maintaining the efficiency and fast convergence of the conventional fb method some numerical results demonstrate the efficiency and accuracy of the new method even for low grazing angle scattering problems

on the discretization of the integral equation describing scattering by rough conducting surfaces numerical simulations of scattering from one dimensional 1 d randomly rough surfaces with pierson moskowitz p m spectra show that if the kernel or propagator matrix with zeros on its diagonal is used in the discretized magnetic field integral equation mfie the results exhibit an excessive sensitivity to the current sampling interval especially for backscattering at low grazing angles lgas though the numerical results reported in this paper were obtained using the method of ordered multiple interactions momi a similar sampling interval sensitivity has been observed when a standard method of moments mom technique is used to solve the mfie a subsequent analysis shows that the root of the problem lies in the correct discretization of the mfie kernel we found that the inclusion of terms proportional to the surface curvature regarded by some authors as an additional correction in the diagonal of the kernel matrix virtually eliminates this sampling sensitivity effect by reviewing the discretization procedure for mfie we show that these curvature terms indeed must be included in the diagonal in order for the propagator matrix to be represented properly the recommended current sampling interval for scattering calculations with p m surfaces is also given

quantum harmonic analysis and geometric invariants we develop two topics in parallel and show their inter relation the first centers on the notion of a fractional differentiable structure on a commutative or a non commutative space we call this studyquantum harmonic analysis the second concerns homotopy invariants for these spaces and is an aspect of non commutative geometry we study an algebra a which will be a banach algebra with unit represented as an algebra of operators on a hilbert space h in order to obtain a geometric interpretation of a we define a derivative on elements of a we do this in a hilbert space context takingdaas a commutatorda q a hereqis a basic self adjoint operator with discrete spectrum increasing sufficiently rapidly that exp q 2has a trace whenever 0 we can define fractional differentiability of order with 0 0 we concentrate on subalgebras a of j which have certain additional covariance properties under a group z2 g acting on h by a unitary representation u g in addition the derivativeqis assumed to be g invariant the geometric interpretation flows from the assumption that elements of a possess an arbitrarily small fractional derivative we study homotopy invariants of a in terms of equivariant entire cyclic cohomology in fact the existence of a fractional derivative on a allows the construction of the cochain jlo which plays the role of the integral of differential forms we give a simple expression for a homotopy invariant zq a g determined by pairing jlo with a g invariant elementa a such thatais a square root of the identity this invariant is zq a g 1 e t2tr u g ae q2 it da dt this representation of the pairing is reminiscent of the heat kernel representation for an index in fact this quantity is an invariant in the following sense we isolate a simple condition on a familyq of differentiations that yields a continuously differentiable family jlo of cochains since zq a g need not be an integer continuity of jlo in is insufficient to prove the constancy of the pairing however the existence of the derivative leads to the existence of the homotopy as a vanishes for a coboundary and asd jlo d is a coboundary our condition onq ensures that zq a g is independent of hence it is a homotopy invariant the theory of zq a g reduces to the study of the radon transform of sequences of certain functions the fractional differentiability properties of elements of a translate into properties of the asymptotics of the sequences of radon transforms the condition that jlofit into the framework of entire cyclic cohomology translates to the existence of some fractional derivative for functions in the algebra under study and in particular the assumption 1 thus the study of fractionally differentiable structures dove tails naturally with the theory of homotopy invariants in our study of quantum harmonic analysis we introduce spaces t of operator valued distributions these spaces are bounded linear operators between sobolev spaces the elements of the interpolation spaces the banach algebras j have derivativesdawhich belong to the spaces t for a certain range of and we extend the theory of the radon transform from products of regularized bounded operators to products of regularized operator valued distributions we sometimes wish to evaluate such an invariant at the endpoint of an interval such as 0 1 where zq a g becomes singular as 0 we discuss in brief a procedure to regularize the endpoint and a method to recover zq a g fully from certain partial information at the endpoint finally we generalize this approach to cover the case whenqcan be split into the sum of independent partsq1 q2 such that q1 q2 2 q1 2 q2 2 here we assume thatq1and q2 2are g invariant but not necessarilyq2 with further assumptions ona the most important being that q1 2 q2 2commutes witha we obtain a modified formula for an invariant namely z qj a g 1 e t2tr u g ae q21 q22 2 itd1a dt

fedosov differentials and catalan numbers the aim of the paper is to establish a non recursive formula for the general solution of fedosov s quadratic fixed point equation fedosov 1994 j diff geom 40 213 38 fedosov s geometrical fixed point equation for a differential is rewritten in a form similar to the functional equation for the generating function of catalan numbers this allows us to guess the solution an adapted example for kaehler manifolds of constant sectional curvature is considered in detail also for every connection on a manifold a familiar classical differential will be introduced

formality and kontsevich duflo type theorems for lie pairs newcommand poly operatorname poly bullet newcommand td operatorname td l a nabla frac 1 2 newcommand cx 1 operatorname tot big gamma lambda bullet a vee otimes r mathcal 1 poly big newcommand cy 1 mathbb h bullet operatorname ce a mathcal 1 poly kontsevich s formality theorem states that there exists an l infty quasi isomorphism from the dgla t poly m of polyvector fields on a smooth manifold m to the dgla d poly m of polydifferential operators on m which extends the classical hochschild kostant rosenberg map in this paper we extend kontsevich s formality theorem to lie pairs a framework which includes a range of diverse geometric contexts such as complex manifolds foliations and mathfrak g manifolds the spaces cx t and cx d associated with a lie pair l a each carry an l infty algebra structure canonical up to l infty isomorphism these two spaces serve as replacements for the spaces of polyvector fields and polydifferential operators respectively their corresponding cohomology groups cy t and cy d admit canonical gerstenhaber algebra structures we establish the following formality theorem for lie pairs there exists an l infty quasi isomorphism from cx t to cx d whose first taylor coefficient is equal to operatorname hkr circ td here td acts on cx t by contraction furthermore we prove a kontsevich duflo type theorem for lie pairs the hochschild kostant rosenberg map twisted by the square root of the todd class of the lie pair l a is an isomorphism of gerstenhaber algebras from cy t to cy d as applications we establish formality theorems and kontsevich duflo type theorems for complex manifolds foliations and mathfrak g manifolds in the case of complex manifolds we recover the kontsevich duflo theorem of complex geometry

frechet algebraic deformation quantization of the poincare disk starting from formal deformation quantization we use an explicit formula for a star product on the poincare disk n to introduce a frechet topology making the star product continuous to this end a general construction of locally convex topologies on algebras with countable vector space basis is introduced and applied several examples of independent interest are investigated as e g group algebras over finitely generated groups and infinite matrices in the case of the star product on n the resulting frechet algebra is shown to have many nice features it is a strongly nuclear kothe space the symmetry group su 1 n acts smoothly by continuous automorphisms with an inner infinitesimal action and evaluation functionals at all points of n are positive functionals

pseudodifferential extension and todd class let m be a closed manifold wodzicki shows that in the stable range the cyclic cohomology of the associative algebra of pseudodierential symbols of order 0 is isomorphic to the homology of the cosphere bundle of m in this article we develop a formalism which allows to calculate that under this isomorphism the radul cocycle corresponds to the poincar e dual of the todd class as an immediate corollary we obtain a purely algebraic proof of the atiyah singer index theorem for elliptic pseudodifferential operators on closed manifolds

weyl manifolds and deformation quantization this paper deals with non commutative objects based on the weyl algebra from the differential geometric point of view we propose to extend familiar notions from manifolds to non commutative objects in this algebraic approach the basic object is not a point of a space but certain sections of bundles

formal series of generalized functions and their application to deformation quantization foundations of the formal series calculus in deformation quantization are discussed several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced the notion of non negativity in formal series calculus is proposed problems with defining quantum states over the set of formal series are analyzed foundations of the formal series calculus in deformation quantization are discussed several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced the notion of non negativity in formal series calculus is proposed problems with defining quantum states over the set of formal series are analyzed

brst cohomology and phase space reduction in deformation quantization in this article we consider quantum phase space reduction when zero is a regular value of the momentum map by analogy with the classical case we define the brst cohomology in the framework of deformation quantization we compute the quantum brst cohomology in terms of a quantum chevalley eilenberg cohomology of the lie algebra on the constraint surface to prove this result we construct an explicit chain homotopy both in the classical and quantum case which is constructed out of a prolongation of functions on the constraint surface we have observed the phenomenon that the quantum brst cohomology cannot always be used for quantum reduction because generally its zero part is no longer a deformation of the space of all smooth functions on the reduced phase space but in case the group action is sufficiently nice e g proper which is the case for all compact lie group actions it is shown for a strongly invariant star product that the brst procedure always induces a star product on the reduced phase space in a rather explicit and natural way simple examples and counterexamples are discussed

the validity of the perturbation approximation for rough surface scattering using a gaussian roughness spectrum the validity of the perturbation approximation for rough surface scattering is examined 1 by comparison with exact results obtained by solving an integral equation and 2 through comparison of low order perturbation predictions with higher order predictions the pressure release boundary condition is assumed and the field quantity calculated is the bistatic scattering cross section a gaussian roughness spectrum is used and the surfaces have height variations in only one direction it is found in general that the condition kh 1 k is the acoustic wavenumber h is the rms surface height is insufficient to guarantee the accuracy of first order or higher order perturbation theory when the surface correlation length l becomes too large or too small with h held fixed higher order perturbation terms can make larger contributions to the scattering cross section than lower order terms an explanation for this result is given the regions of validity for low order perturbation theory are also given th

quantum riemann surfaces i the unit disc we construct a non commutative algebra c mu bar u which is a quantum deformation of the algebra of continuous functions on the closed unit disc bar u c mu bar u is generated by the toeplitz operators on a suitable hilbert space of holomorphic functions onu

low grazing angle scattering from rough surfaces in a duct formed by a linear square refractive index profile the problem of rough surface scattering and propagation over rough terrain in a ducting environment has been receiving considerable attention in the literature one popular method of modeling this problem is the parabolic wave equation pwe method an alternative method is the boundary integral equation bie method the implementation of the bie in inhomogeneous media ducting environments is not straightforward however since the green s function for such a medium is not usually known in this paper a closed form approximation of the green s function for a two dimensional 2 d ducting environment formed by a linear square refractive index profile is derived using asymptotic techniques this green s function greatly facilitates the use of the bie approach to study low grazing angle lga rough surface scattering and propagation over rough surfaces in the aforementioned ducting environment this paper demonstrates how the bie method can model the combined effects of surface roughness and medium inhomogeneity in a very rigorous fashion furthermore it illustrates its capability of accurately predicting scattering in all directions including backscattering the boundary integral equation of interest is solved via the method of ordered multiple interactions momi which eliminates the requirements of matrix storage and inversion and hence allows the application of the bie method to very long rough surfaces

on the chern character of a theta summable fredholm module on montre qu il est possible de simplifier la theorie de connes du caractere de chern a partir d une k homologie d une algebre de banach vers une cohomologie cyclique entiere

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

the deformation quantizations of the hyperbolic plane we describe the space of all invariant both formal and non formal deformation quantizations on the hyperbolic plane mathbb d as solutions of the evolution of a second order hyperbolic differential operator the construction is entirely explicit and relies on non commutative harmonic analytical techniques on symplectic symmetric spaces the present work presents a unified method producing every quantization of mathbb d and provides in the 2 dimensional context an exact solution to weinstein s wkb quantization program within geometric terms the construction reveals the existence of a metric of lorentz signature canonically attached or dual to the geometry of the hyperbolic plane through the quantization process

an algebraic index theorem for orbifolds abstract using the concept of a twisted trace density on a cyclic groupoid a trace is constructed on a formal deformation quantization of a symplectic orbifold an algebraic index theorem for orbifolds follows as a consequence of a local riemann roch theorem for such densities in the case of a reduced orbifold this proves a conjecture by fedosov schulze and tarkhanov finally it is shown how the kawasaki index theorem for elliptic operators on orbifolds follows from this algebraic index theorem

convergence of the wick star product we construct a frechet space as a subspace of c omega mathbb c n where the wick star product converges and is continuous the resulting frechet algebra mathcal a is studied in detail including a representation of mathcal a in the bargmann fock space and a discussion of star exponentials and coherent states

homogeneous fedosov star products on cotangent bundles i weyl and standard ordering with differential operator representation in this paper we construct homogeneous star products of weyl type on every cotangent bundle t q by means of the fedosov procedure using a symplectic torsion free connection on t q homogeneous of degree zero with respect to the liouville vector field by a fibrewise equivalence transformation we construct a homogeneous fedosov star product of standard ordered type equivalent to the homogeneous fedosov star product of weyl type representations for both star product algebras by differential operators on functions on q are constructed leading in the case of the standard ordered product to the usual standard ordering prescription for smooth complex valued functions on t q polynomial in the momenta where an arbitrary fixed torsion free connection 0 on q is used motivated by the flat case t n another homogeneous star product of weyl type corresponding to the weyl ordering prescription is constructed the example of the cotangent bundle of an arbitrary lie group is explicitly computed and the star product given by gutt is rederived in our approach

on representations of star product algebras over cotangent spaces on hermitian line bundles abstract for every formal power series b of closed two forms on a manifold q and every value of an ordering parameter 0 1 we construct a concrete star product b on the cotangent bundle t q the star product b is associated to the symplectic form on t q given by the sum of the canonical symplectic form and the pull back of b to t q deligne s characteristic class of b is calculated and shown to coincide with the formal de rham cohomology class of b divided by i therefore every star product on t q corresponding to the canonical poisson bracket is equivalent to some b it turns out that every b is strongly closed in this paper we also construct and classify explicitly formal representations of the deformed algebra as well as operator representations given by a certain global symbol calculus for pseudodifferential operators on q moreover we show that the latter operator representations induce the formal representations by a certain taylor expansion we thereby obtain a compact formula for the wkb expansion

on the homology of algebras of whitney functions over subanalytic sets in this article we study several homology theories of the algebra e x of whitney functions over a subanalytic set x r n with a view towards noncommutative geometry using a localization method going back to teleman we prove a hochschild kostant rosenberg type theorem for e x when x is a regular subset of r n having regularly situated diagonals this includes the case of subanalytic x we also compute the hochschild cohomology of e x for a regular set with regularly situated diagonals and derive the cyclic and periodic cyclic theories it is shown that the periodic cyclic homology coincides with the de rham cohomology thus generalizing a result of feigin tsygan motivated by the algebraic de rham theory of grothendieck we finally prove that for subanalytic sets the de rham cohomology of e x coincides with the singular cohomology for the proof of this result we introduce the notion of a bimeromorphic subanalytic triangulation and show that every bounded subanalytic set admits such a triangulation contents

formal symplectic groupoid of a deformation quantization we give a self contained algebraic description of a formal symplectic groupoid over a poisson manifold m to each natural star product on m we then associate a canonical formal symplectic groupoid over m finally we construct a unique formal symplectic groupoid with separation of variables over an arbitrary kahler poisson manifold

a formality theorem for hochschild chains abstract we prove tsygan s formality conjecture for hochschild chains of the algebra of functions on an arbitrary smooth manifold m using the fedosov resolutions proposed in math qa 0307212 and the formality quasi isomorphism for hochschild chains of r y 1 y d proposed in paper math qa 0010321 by shoikhet this result allows us to describe traces on the quantum algebra of functions on an arbitrary poisson manifold

deformation quantization and the baum connes conjecture alternative titles of this paper would have been index theory without index or the baum connes conjecture without baum

on the use of finite surfaces in the numerical prediction of rough surface scattering method of moments mom based monte carlo calculations are widely used in determining the average radar cross section of randomly rough surfaces it is desirable in these numerical calculations to truncate the scattering surface into as short a length as possible to minimize the solution time however truncating the surface tends to change the solution for the surface fields near the truncation points and may alter the scattered far fields in this paper these end effect errors are examined for one dimensional i e grooved or corduroy surfaces which are gaussian distributed in height and have either a gaussian or a pierson moskowitz spectra in the case of the pierson moskowitz type surface it is shown that a relatively short surface of 80 120 wavelengths can be used to obtain the average backscattered radar cross section for backscattering angles as large as 60 spl deg from normal for a comparatively smooth gaussian surface on the other hand its is shown that the truncation effects can be very significant at moderate backscattering angles also great care should be taken when examining the scattering from gaussian surfaces which are dominated by specular scattering it is shown that in this situation a very large number of calculations may be needed to obtain a good numerical average

formal gns construction and states in deformation quantization in this paper we develop a method of constructing hilbert spaces and the representation of the formal algebra of quantum observables in deformation quantization which is an analog of the well known gns construction for complex c algebras in this approach the corresponding positive linear functionals states take their values not in the field of complex numbers but in a suitable extension field of the field of formal complex laurent series in the formal parameter by using the algebraic and topological properties of these fields we prove that this construction makes sense and show in physical examples that standard representations such as the bargmann and schrodinger representation come out correctly both formally and in a suitable convergence scheme for certain hamiltonian functions contained in the gel fand ideal of the positive functional a formal solution to the time dependent schrodinger equation is shown to exist moreover we show that for every kahler manifold equipped with the fedosov star product of wick type all the classical delta functionals are positive and give rise to some formal bargmann representation of the deformed algebra

quantization of kahler manifolds ii we use berezin s dequantization procedure to define a formal product on a dense subalgebra of the algebra ofsmooth functions on a compact homogeneous kahler manifold m we prove that this formal product isconvergent when m isa hermitian symmetric space 1993 american mathematical society

quantization of multiply connected manifolds the standard berezin toeplitz geometric quantization of a compact kahler manifold is restricted by integrality conditions these restrictions can be circumvented by passing to the universal covering space provided that the lift of the symplectic form is exact i relate this construction to the baum connes assembly map and prove that it gives a strict quantization of the original manifold i also propose a further generalization classify the required structure and provide a means of computing the resulting algebras these constructions involve twisted group c algebras of the fundamental group which are determined by a group cocycle constructed from the cohomology class of the symplectic form this provides an algebraic counterpart to the morita equivalence of a symplectic manifold with its fundamental group

tapered wave with dominant polarization state for all angles of incidence typical applications of the method of moments mom to rough surface three dimensional 3 d electromagnetic scattering require a truncation of the surface considered and call for a tapered incident wave it is shown how such a wave can be constructed as a superposition of plane waves avoiding problems near both normal and grazing incidence and providing clean footprints and clear polarization at all angles of incidence the proposed special choice of polarization vectors removes an irregularity at the origin of the wavenumber space and leads to a least squared error property of the wave issues in the application to 3 d scattering from an object over a rough surface are discussed approximate 3 d scalar and vector tapered waves which can be evaluated without resorting to any numerical integrations are derived and important limitations to the accuracy and applicability of these approximations are pointed out

on the core of multiple longest traveling salesman games in this paper we introduce multiple longest traveling salesman mlts games an mlts game arises from a network in which a salesman has to visit each node player precisely once except to his home location in such an order that maximizes the total reward first it is shown that the value of a coalition of an mlts game is determined by taking the maximum of suitable combinations of one and two person coalitions secondly it is shown that mlts games with five or less players have a nonempty core however a six player mlts game may have an empty core for the special instance in which the reward between a pair of nodes is equal to 0 or 1 we provide relations between the structure of the core and the underlying network

a new numerical method for rough surface scattering calculations a new approach to solving the magnetic field integral equation mfie for the current induced on a infinite perfectly conducting rough surface is presented by splitting the propagator matrix into contributions from the left and from the right of the point of observation a second kind integral equation can be formed with a new born term and a new kernel following discretization of this new integral equation the unknown currents can be determined more rapidly and with significantly less storage requirements than conventional lu decomposition where the time saving factor is roughly n 3 where n is the number of current samples on the surface and the usual storage requirements associated with matrix inversion are eliminated while the new born term is usually adequate for scattered field calculations the new discretized integral equation can be iterated to amy desired accuracy with no apparent convergence problems results are presented for one dimensional rough surfaces with rms heights exceeding one wavelength and rms slopes exceeding 40 which illustrate the robustness of the new born term

cyclic cocycles on deformation quantizations and higher index theorems abstract we construct a nontrivial cyclic cocycle on the weyl algebra of a symplectic vector space using this cyclic cocycle we construct an explicit local quasi isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof we give a new proof of nest tsygan s algebraic higher index theorem by computing the pairing between such cyclic cocycles and the k theory of the formal deformation quantization furthermore we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold as an application we obtain the analytic higher index theorem of connes moscovici and its extension to orbifolds

cyclic cohomology of the weyl algebra abstract we give an explicit formula for sp 2 n basic representatives of the cyclic cohomology of the weyl algebra h c a 2 n as an application we prove a generalization of a theorem of nest and tsygan concerning the relation of the todd class and the cyclic cohomology of the differential operators on a complex manifold

algebraic index theorem we prove the atiyah singer index theorem where the algebra of pseudodifferential operators is replaced by an arbitrary deformation quantization of the algebra of functions on a symplectic manifold

quantum hall effect on the hyperbolic plane in this paper we study both the continuous model and the discrete model of the quantum hall effect qhe on the hyperbolic plane the hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables we define a twisted analogue of the kasparov map which enables us to use the pairing between k theory and cyclic cohomology theory to identify this geometric invariant with a topological index thereby proving the integrality of the hall conductivity in this case

the characteristic classes of morita equivalent star products on symplectic manifolds in this paper we give a complete characterization of morita equivalent star products on symplectic manifolds in terms of their characteristic classes two star products and on m are morita equivalent if and only if there exists a symplectomorphism colon m m such that the relative class t is 2 i integral for star products on cotangent bundles we show that this integrality condition is related to dirac s quantization condition for magnetic charges

characters of cycles equivariant characteristic classes and fredholm modules we derive simple explicit formula for the character of a cycle in the connes b b bicomplex of cyclic cohomology and apply it to write formulas for the equivariant chern character and characters of finitely summable bounded fredholm modules

scattering from very large randomly rough surfaces using a markov random field equivalent current a markov random field mrf model is employed to learn the statistical properties of an equivalent current situated above a rough surface where this equivalent current represents near field electromagnetic scattered fields the mrf parameters are learned by considering numerical scattering from a relatively small rough surface which can be solved efficiently via existing numerical methods the mrf parameters may then be used to synthesize multiple realizations of the equivalent current associated with scattering from a much larger rough surface these equivalent currents may be used to efficiently calculate the far field scattered field statistics for large surfaces the advantages of this approach are manifested in the fact that once the mrf parameters are learned a forward model is no longer needed to generate random realizations of the equivalent currents and the mrf model can be employed to generate equivalent surfaces of size beyond the capability of existing numerical models to improve the accuracy of the mrf model a narrowband filter is used to preprocess the computed current distributions prior to mrf model training one dimensional rough surfaces are considered here to demonstrate the idea and the method of ordered multiple interactions momi is employed to perform the numerical forward modeling promising mrf generated results are demonstrated with comparison to direct momi solutions

traveling salesman games in this paper we discuss the problem of how to divide the total cost of a round trip along several institutes among the institutes visited we introduce two types of cooperative games fixed route traveling salesman games and traveling salesman games as a tool to attack this problem under very mild conditions we prove that fixed route traveling salesman games have non empty cores if the fixed route is a solution of the classical traveling salesman problem core elements provide us with fair cost allocations a traveling salesman game may have an empty core even if the cost matrix satisfies the triangle inequality in this paper we introduce a class of matrices defining ts games with non empty cores

explicit formulas for noncommutative deformations of cpn and chn we give explicit expressions of a deformation quantization with separation of variables for cpn and chn this quantization method is one of the ways to perform a deformation quantization of kahler manifolds which is introduced by karabegov star products are obtained as explicit formulas in all order in the noncommutative parameter we also give the fock representations of the noncommutative cpn and chn

free products cyclic homology and the gauss manin connection abstract we use the techniques of cuntz and quillen to present a new approach to periodic cyclic homology our construction is based on a t d t i a noncommutative equivariant de rham complex of an associative algebra a here d is the karoubi de rham differential and i is an operation analogous to contraction with a vector field as a byproduct we give a simple explicit construction of the gauss manin connection introduced earlier by e getzler on the relative periodic cyclic homology of a flat family of associative algebras over a central base ring we introduce and study free product deformations of an associative algebra a new type of deformation over a not necessarily commutative base ring natural examples of free product deformations arise from preprojective algebras and group algebras for compact surface groups

non formal star exponential on contracted one sheeted hyperboloids in this paper we exhibit the non formal star exponential of the lie group sl 2 r realized geometrically on the curvature contraction of its one sheeted hyperboloid orbits endowed with its natural non formal star product it is done by a direct resolution of the defining equation of the star exponential and produces an expression with bessel functions this yields a continuous group homomorphism from sl 2 r into the von neumann algebra of multipliers of the hilbert algebra associated to this natural star product as an application we prove a new identity on bessel functions

involutions and representations for reduced quantum algebras abstract in the context of deformation quantization there exist various procedures to deal with the quantization of a reduced space m red we shall be concerned here mainly with the classical marsden weinstein reduction assuming that we have a proper action of a lie group g on a poisson manifold m with a moment map j for which zero is a regular value for the quantization we follow bordemann et al 2000 6 with a simplified approach and build a star product red on m red from a strongly invariant star product on m the new questions which are addressed in this paper concern the existence of natural involutions on the reduced quantum algebra and the representation theory for such a reduced algebra we assume that is hermitian and we show that the choice of a formal series of smooth densities on the embedded coisotropic submanifold c j 1 0 with some equivariance property defines a involution for red on the reduced space looking into the question whether the corresponding involution is the complex conjugation which is a involution in the marsden weinstein context yields a new notion of quantized modular class we introduce a left c m submodule and a right c m red red submodule c cf c of c c we define on it a c m red valued inner product and we establish that this gives a strong morita equivalence bimodule between c m red and the finite rank operators on c cf c the crucial point is here to show the complete positivity of the inner product we obtain a rieffel induction functor from the strongly non degenerate representations of c m red red on pre hilbert right d modules to those of c m for any auxiliary coefficient algebra d over c

strings in ads3 and the sl 2 r wzw model i the spectrum in this paper we study the spectrum of bosonic string theory on ads3 we study classical solutions of the sl 2 r wzw model including solutions for long strings with nonzero winding number we show that the model has a symmetry relating string configurations with different winding numbers we then study the hilbert space of the wzw model including all states related by the above symmetry this leads to a precise description of long strings we prove a no ghost theorem for all the representations that are involved and discuss the scattering of the long string

geometric quantization of vector bundles and the correspondence with deformation quantization i repeat my definition for quantization of a vector bundle for the cases of the toeplitz and geometric quantizations of a compact kahler manifold i give a construction for quantizing any smooth vector bundle which depends functorially on a choice of connection on the bundle