Related papers: When Poisson and Moyal Brackets are equal?

Given a smooth oriented manifold $M$ with non-empty boundary, we study the Pontryagin algebra $A=H_\ast(\Omega )$ where $ \Omega $ is the space of loops in $M$ based at a distinguished point of $ \partial M$. Using the ideas of string…

The Lie algebroids are generalization of the Lie algebras. They arise, in particular, as a mathematical tool in investigations of dynamical systems with the first class constraints. Here we consider canonical symmetries of Hamiltonian…

We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of…

We deduce a kernel that allows the Moyal quantization of the cylinder (as phase space) by means of the Stratonovich-Weyl correspondence.

Felder and Kazhdan conjecture that the local cohomology in the classical Batalin-Vilkovisky formalism vanishes in sufficiently negative degrees. This hypothesis is violated by the $N=1$ spinning particle. By Barnich-Grigoriev, this…

Weyl-von Neumann Theorem asserts that two bounded self-adjoint operators $A,B$ on a Hilbert space $H$ are unitarily equivalent modulo compacts, i.e., $uAu^*+K=B$ for some unitary $u\in \mathcal{U}(H)$ and compact self-adjoint operator $K$,…

It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented. On the trivialized space, the canonical symplectic…

If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak c$ and Weyl group $W$, it is shown that there is a natural morphism of Poisson schemes $\mathfrak c \oplus {\mathfrak c}^*/W \to V\oplus V^*/\!\!/\!\!/ G$. This morphism…

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic…

Quantization is not a straightforward proposition, as shown by Groenewold's and Van Hove's discovery, more than fifty years ago, of an "obstruction" to quantization. Their "no-go theorems" assert that it is impossible to consistently…

We provide an answer to the long standing problem of mixing quantum and classical dynamics within a single formalism. The construction is based on p-mechanical derivation (quant-ph/0212101, quant-ph/0304023) of quantum and classical…

For a derivation d of a commutative Noetherian complex algebra A, a homeomorphism is established between the prime spectrum of the Ore extension A[z;d] and the Poisson prime spectrum of the polynomial algebra A[z] endowed with the Poisson…

In this note the notion of Poisson brackets in Kontsevich's "Lie World" is developed. These brackets can be thought of as "universally" defined classical Poisson structures, namely formal expressions only involving the structure maps of a…

In this paper we consider structures of complex Poisson brackets on the space of smooth functions in a $n$-dimensional complex manifold generated by the $(1,1)$-form $d=\partial+\overline{\partial}$-closed and non-degenerate (with…

We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing…

Canonical structure of the space-time symmetric analogue of the Hamiltonian formalism in field theory based on the De Donder-Weyl (DW) theory is studied. In $n$ space-time dimensions the set of $n$ polymomenta is associated to the…

A normal form transformation is carried out on the operators of a complete set of commuting observables in a multidimensional, integrable quantum system, mapping them by unitary conjugation into functions of the harmonic oscillators in the…

Let M be a paracompact smooth manifold, A a Weil algebra and M^{A} the associated Weil bundle. In this paper, we give a characterization of hamiltonian field on M^{A} in the case of Poisson manifold and of Symplectic manifold.

Let $(R^{\vee},R)$ be a dual pair of Hopf algebras in the category of Yetter-Drinfeld modules over a Hopf algebra $H$ with bijective antipode. We show that there is a braided monoidal isomorphism between rational left Yetter-Drinfeld…

In this paper we introduce a kind of "noncommutative neighbourhood" of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of…