We compute the Poisson bracket relations for the monodromy matrix of the auxiliary linear problem. If the basic Poisson brackets of the model contain derivatives, this computation leads to a peculiar kind of symmetry breaking which accounts for a 'spontaneous quantiza-tion' of the underlying global gauge group. A classification of possible patterns of symmetry breaking is outlined.

Abstract Nambu dynamics is a generalized Hamiltonian of more than two variables, whose time evolutions are given by the bracket, generalization canonical Poisson bracket. can always be represented in form noncanonical defining bracket means For evolution to consistent, must satisfy fundamental identity, while Jacobi identity. However, many degrees freedom systems, it well known that identity do...

New realizations of observables in dynamical systems with second class constraints. Abstract In the Dirac bracket approach to dynamical systems with second class constrains the observables are represented by elements of a quotient Dirac bracket algebra. We describe the constraints which allow to construct families of new realizations of this algebra. The realizations are obtained as quotients o...

The constrained Modified KP hierarchy is considered from the viewpoint of modification. It is shown that its second Poisson bracket, which has a rather complicated form, is associated to a vastly simpler bracket via Miura-type map. The similar results are established for a natural reduction of MKP. † Supported by Beca para estancias temporales de doctores y tecnólogos extranjeros en España: SB9...

This paper investigates the Hamiltonian structure and Poisson bracket formulation of a higher-order, geometrically-exact Cosserat type beam with deforming cross-section in terms canonically conjugate variables.

New realizations of observables in dynamical systems with second class constraints. Abstract In the Dirac bracket approach to dynamical systems with second class constrains the observables are represented by elements of a quotient Dirac bracket algebra. We describe the constraints which allow to construct families of new realizations of this algebra. The realizations are obtained as quotients o...

The product of quantum mechanics is defined as the ordinary multiplication followed by the application of superoperator that orders involved operators. The operator version of Poisson bracket is defined being the Lie bracket which substitutes commutator in the von Neumann equation. These result in obstruction free quantization, with the ordering rule which coincides with Weyl ordering rule. e-m...

In this paper we introduce two classes of Poisson brackets on algebras (or on sheaves of algebras). We call them locally free and nonsingular Poisson brackets. Using the Fedosov’s method we prove that any locally free nonsingular Poisson bracket can be quantized. In particular, it follows from this that all Poisson brackets on an arbitrary field of characteristic zero can be quantized. The well...