Related papers: Quantization of Planck's Constant

Poisson transversals are those submanifolds in a Poisson manifold which intersect all symplectic leaves transversally and symplectically. In a previous note we proved a normal form theorem around such submanifolds. In this communication, we…

The canonical formalism in classical theory of QCD is constructed on a space-like hypersurface. The Poisson bracket on the space-like hypersurface is defined and it plays an important role to describe every algebraic relation in the…

The Adler-Gelfand-Dikii Poisson structure arises naturally in the study of $n$-th order differential operators on the circle and plays a central role in Poisson geometry and integrable systems. Let $G$ be one of the Lie groups…

We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative…

We give a mathematical definition of some path integrals, emphasizing those relevant to the quantization of symplectic manifolds (and more generally, Poisson manifolds) $\unicode{x2013}$ in particular, the coherent state path integral. We…

Quantum Groups can be constructed by applying the quantization by deformation procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to develop an understanding of these structures by investigating dynamical systems…

We discuss the integrability of Jacobi manifolds by contact groupoids, and then look at what the Jacobi point of view brings new into Poisson geometry. In particular, using contact groupoids, we prove a Kostant-type theorem on the…

Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…

This note explains a construction of a Poisson manifold whose symplectic foliation describes a deformation of a moduli space of meromorphic connections with unramified irregular singularities. In particular, this deformation of the moduli…

On a complex symplectic manifold, we construct the stack of quantization-deformation modules, that is, (twisted) modules of microdifferential operators with an extra central parameter, a substitute to the lack of homogeneity. We also…

We generalize the notion of trace to the Kontsevich quantization algebra and show that for all Poisson manifolds representable by quotients of a symplectic manifold by a Hamiltonian action of a nilpotent Lie group, the trace is given by…

We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of…

A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…

We establish a 1:1 correspondence between Poisson-Lie group actions on integrable Poisson manifolds and twisted multiplicative hamiltonian actions on source 1-connected symplectic groupoids. For an action of a Poisson-Lie group $G$ on a…

In recent years methods for the integration of Poisson manifolds and of Lie algebroids have been proposed, the latter being usually presented as a generalization of the former. In this note it is shown that the latter method is actually…

In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…

The main idea of this note is to describe the integration procedure for poly-Poisson structures, that is, to find a poly-symplectic groupoid integrating a poly-Poisson structure, in terms of topological field theories, namely via the…

Superimposed D-branes have matrix-valued functions as their transverse coordinates, since the latter take values in the Lie algebra of the gauge group inside the stack of coincident branes. This leads to considering a classical dynamics…

Let (E,D,P) be a flat vector bundle with a parabolic structure over a punctured Riemann surface, (M,g). We consider a deformation of the harmonic metric equation which we call the Poisson metric equation. This equation arises naturally as…

In this note the long standing problem of the definition of a Poisson bracket in the framework of a multisymplectic formulation of classical field theory is solved. The new bracket operation can be applied to forms of arbitary degree.…