342 research outputs found
BRST theory without Hamiltonian and Lagrangian
We consider a generic gauge system, whose physical degrees of freedom are
obtained by restriction on a constraint surface followed by factorization with
respect to the action of gauge transformations; in so doing, no Hamiltonian
structure or action principle is supposed to exist. For such a generic gauge
system we construct a consistent BRST formulation, which includes the
conventional BV Lagrangian and BFV Hamiltonian schemes as particular cases. If
the original manifold carries a weak Poisson structure (a bivector field giving
rise to a Poisson bracket on the space of physical observables) the generic
gauge system is shown to admit deformation quantization by means of the
Kontsevich formality theorem. A sigma-model interpretation of this quantization
algorithm is briefly discussed.Comment: 19 pages, minor correction
Volume preserving multidimensional integrable systems and Nambu--Poisson geometry
In this paper we study generalized classes of volume preserving
multidimensional integrable systems via Nambu--Poisson mechanics. These
integrable systems belong to the same class of dispersionless KP type equation.
Hence they bear a close resemblance to the self dual Einstein equation. All
these dispersionless KP and dToda type equations can be studied via twistor
geometry, by using the method of Gindikin's pencil of two forms. Following this
approach we study the twistor construction of our volume preserving systems
BRST analysis of general mechanical systems
We study the groups of local BRST cohomology associated to the general
systems of ordinary differential equations, not necessarily Lagrangian or
Hamiltonian. Starting with the involutive normal form of the equations, we
explicitly compute certain cohomology groups having clear physical meaning.
These include the groups of global symmetries, conservation laws and Lagrange
structures. It is shown that the space of integrable Lagrange structures is
naturally isomorphic to the space of weak Poisson brackets. The last fact
allows one to establish a direct link between the path-integral quantization of
general not necessarily variational dynamics by means of Lagrange structures
and the deformation quantization of weak Poisson brackets.Comment: 38 pages, misprints corrected, references and the Conclusion adde
A new approach to the Lenard-Magri scheme of integrability
We develop a new approach to the Lenard-Magri scheme of integrability of
bi-Hamiltonian PDE's, when one of the Poisson structures is a strongly
skew-adjoint differential operator.Comment: 20 page
Poisson-Nijenhuis structures on quiver path algebras
We introduce a notion of noncommutative Poisson-Nijenhuis structure on the
path algebra of a quiver. In particular, we focus on the case when the Poisson
bracket arises from a noncommutative symplectic form. The formalism is then
applied to the study of the Calogero-Moser and Gibbons-Hermsen integrable
systems. In the former case, we give a new interpretation of the bihamiltonian
reduction performed in [3].Comment: 23 page
Bihamiltonian cohomology of KdV brackets
Using spectral sequences techniques we compute the bihamiltonian cohomology
groups of the pencil of Poisson brackets of dispersionless KdV hierarchy. In
particular this proves a conjecture of Liu and Zhang about the vanishing of
such cohomology groups.Comment: 16 pages. v2: corrected typos, in particular formulas (28), (78
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