Related papers: Trace Functionals of the Kontsevich Quantization

A general approach to proving that the length spectrum of a compact Riemannian manifold is an invariant of the Laplace spectrum comes from considering the wave trace, a spectrally determined tempered distribution. The Poisson relation…

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. Trace representation can help us producing the sequences efficiently and analyzing their…

With techniques borrowed from quantum information theory, we develop a method to systematically obtain operator inequalities and identities in several matrix variables. These take the form of trace polynomials: polynomial-like expressions…

We describe an efficient construction of a canonical non-commutative deformation of the algebraic functions on the moduli spaces of flat connections on a Riemann surface. We show that this algebra, which is a variant of the quantum moduli…

We show that various notions of integrability for Poisson brackets are all equivalent, and we give the precise obstructions to integrating Poisson manifolds. We describe the integration as a symplectic quotient, in the spirit of the Poisson…

We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group $K$ on a manifold $M$ descends to an integrable system on a dense open subset of the quotient Poisson space $M/K$. The higher…

There is a simple and natural quantization of differential forms on odd Poisson supermanifolds, given by the relation [f,dg]={f,g} for any two functions f and g. We notice that this non-commutative differential algebra has a geometrical…

The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An…

We propose a Poisson-Lie analog of the symplectic induction procedure, using an appropriate Poisson generalization of the reduction of symplectic manifolds with symmetry. Having as basic tools the equivariant momentum maps of Poisson…

Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensional affine manifolds. The calculus of Kontsevich graphs can be…

In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic…

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…

Let $\gp$ be a finite group acting on a compact manifold $M$ and $\maA(M)$ denote the algebra of classical complete symbols on $M$. We determine all traces on the cross-product algebra $\maA(M) \rtimes \Gamma$. These traces appear as…

Let $(M,J,\omega)$ be a quantizable compact K\"ahler manifold, with quantizing Hermitian line bundle $(A,h)$, and associated Hardy space $H(X)$, where $X$ is the unit circle bundle. Given a collection of $r$ Poisson commuting quantizable…

It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that noncommutative gauge theories on more…

Let $G$ be a semisimple Lie group with finite component group, and let $K<G$ be a maximal compact subgroup. We obtain a quantisation commutes with reduction result for actions by $G$ on manifolds of the form $M = G\times_K N$, where $N$ is…

Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via…

In quantum physics, the operators associated with the position and the momentum of a particle are unbounded operators and $C^*$-algebraic quantisation does therefore not deal with such operators. In the present article, I propose a…

Let M be a closed manifold and let CL(M) be the algebra of classical pseudodifferential operators. The aim of this note is to classify trace functionals on the subspaces CL^a(M) of CL(M) of operators of order a. CL^a(M) is a CL^0(M)-module…

This note introduces the construction of relational symplectic groupoids as a way to integrate every Poisson manifold. Examples are provided and the equivalence, in the integrable case, with the usual notion of symplectic groupoid is…