1,089 research outputs found
BRST Formalism and Zero Locus Reduction
In the BRST quantization of gauge theories, the zero locus of the BRST
differential carries an (anti)bracket whose parity is opposite to that of
the fundamental bracket. We show that the on-shell BFV/BV gauge symmetries are
in a 1:1 correspondence with Hamiltonian vector fields on , and
observables of the BRST theory are in a 1:1 correspondence with characteristic
functions of the bracket on . By reduction to the zero locus, we obtain
relations between bracket operations and differentials arising in different
complexes (the Gerstenhaber, Schouten, Berezin-Kirillov, and Sklyanin
brackets); the equation ensuring the existence of a nilpotent vector field on
the reduced manifold can be the classical Yang-Baxter equation. We also
generalize our constructions to the bi-QP-manifolds which from the BRST theory
viewpoint corresponds to the BRST-anti-BRST-symmetric quantization.Comment: 21 pages, latex2e, several modifications have been made, main content
remains unchange
Isomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket
One may introduce at least three different Lie algebras in any Lagrangian
field theory : (i) the Lie algebra of local BRST cohomology classes equipped
with the odd Batalin-Vilkovisky antibracket, which has attracted considerable
interest recently~; (ii) the Lie algebra of local conserved currents equipped
with the Dickey bracket~; and (iii) the Lie algebra of conserved, integrated
charges equipped with the Poisson bracket. We show in this paper that the
subalgebra of (i) in ghost number and the other two algebras are
isomorphic for a field theory without gauge invariance. We also prove that, in
the presence of a gauge freedom, (ii) is still isomorphic to the subalgebra of
(i) in ghost number , while (iii) is isomorphic to the quotient of (ii) by
the ideal of currents without charge. In ghost number different from , a
more detailed analysis of the local BRST cohomology classes in the Hamiltonian
formalism allows one to prove an isomorphism theorem between the antibracket
and the extended Poisson bracket of Batalin, Fradkin and Vilkovisky.Comment: 36 pages Latex fil
Generalized Classical BRST Cohomology and Reduction of Poisson Manifolds
In this paper, we formulate a generalization of the classical BRST
construction which applies to the case of the reduction of a poisson manifold
by a submanifold. In the case of symplectic reduction, our procedure
generalizes the usual classical BRST construction which only applies to
symplectic reduction of a symplectic manifold by a coisotropic submanifold,
\ie\ the case of reducible ``first class'' constraints. In particular, our
procedure yields a method to deal with ``second-class'' constraints. We
construct the BRST complex and compute its cohomology. BRST cohomology vanishes
for negative dimension and is isomorphic as a poisson algebra to the algebra of
smooth functions on the reduced poisson manifold in zero dimension. We then
show that in the general case of reduction of poisson manifolds, BRST
cohomology cannot be identified with the cohomology of vertical differential
forms.Comment: 3
BRST structure of non-linear superalgebras
In this paper we analyse the structure of the BRST charge of nonlinear
superalgebras. We consider quadratic non-linear superalgebras where a
commutator (in terms of (super) Poisson brackets) of the generators is a
quadratic polynomial of the generators. We find the explicit form of the BRST
charge up to cubic order in Faddeev-Popov ghost fields for arbitrary quadratic
nonlinear superalgebras. We point out the existence of constraints on structure
constants of the superalgebra when the nilpotent BRST charge is quadratic in
Faddeev-Popov ghost fields. The general results are illustrated by simple
examples of superalgebras.Comment: 15 pages, Latex, references added, misprints corrected, comments
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A BRST Analysis of -symmetries
We perform a classical BRST analysis of the symmetries corresponding to a
generic -algebra. An essential feature of our method is that we write the
-algebra in a special basis such that the algebra manifestly has a
``nested'' set of subalgebras where the subalgebra consists of
generators of spin , respectively. In the new basis the
BRST charge can be written as a ``nested'' sum of nilpotent BRST charges.
In view of potential applications to (critical and/or non-critical) -string
theories we discuss the quantum extension of our results. In particular, we
present the quantum BRST-operator for the -algebra in the new basis. For
both critical and non-critical -strings we apply our results to discuss the
relation with minimal models.Comment: 32 pages, UG-4/9
BRST Structures and Symplectic Geometry on a Class of Supermanifolds
By investigating the symplectic geometry and geometric quantization on a
class of supermanifolds, we exhibit BRST structures for a certain kind of
algebras. We discuss the undeformed and q-deformed cases in the classical as
well as in the quantum cases.Comment: 14 pages, Late
Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
We introduce the concept of a variational tricomplex, which is applicable
both to variational and non-variational gauge systems. Assigning this
tricomplex with an appropriate symplectic structure and a Cauchy foliation, we
establish a general correspondence between the Lagrangian and Hamiltonian
pictures of one and the same (not necessarily variational) dynamics. In
practical terms, this correspondence allows one to construct the generating
functional of weak Poisson structure starting from that of Lagrange structure.
As a byproduct, a covariant procedure is proposed for deriving the classical
BRST charge of the BFV formalism by a given BV master action. The general
approach is illustrated by the examples of Maxwell's electrodynamics and chiral
bosons in two dimensions.Comment: 34 pages, v2 minor correction
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