85 research outputs found
Quantum antibrackets
A binary expression in terms of operators is given which satisfies all the
quantum counterparts of the algebraic properties of the classical antibracket.
This quantum antibracket has therefore the same relation to the classical
antibracket as commutators to Poisson brackets. It is explained how this
quantum antibracket is related to the classical antibracket and the
\Delta-operator in the BV-quantization. Higher quantum antibrackets are
introduced in terms of generating operators, which automatically yield all
their subsequent Jacobi identities as well as the consistent Leibniz' rules.Comment: 12 pages,Latexfile,Corrected misprint in (43
General Triplectic Quantization
The general structure of the Sp(2) covariant version of the field-antifield
quantization of general constrained systems in the Lagrangian formalism, the so
called triplectic quantization, as presented in our previous paper with
A.M.Semikhatov is further generalized and clarified.
We present new unified expressions for the generating operators which are
more invariant and which yield a natural realization of the operator V^a and
provide for a geometrical explanation for its presence. This V^a operator
provides then for an invariant definition of a degenerate Poisson bracket on
the triplectic manifold being nondegenerate on a naturally defined submanifold.
We also define inverses to nondegenerate antitriplectic metrics and give a
natural generalization of the conventional calculus of exterior differential
forms which e g explains the properties of these inverses. Finally we define
and give a consistent treatment of second class hyperconstraints.Comment: 19 pages,latexfile,improved wedge produc
Completely anticanonical form of Sp(2)-symmetric Lagrangian quantization
The Sp(2)-symmetric Lagrangian quantization scheme is represented in a
completely anticanonical form. Antifields are assigned to all field variables
including former "parametric" ones \pi^{Aa}. The antibrackets (F, G)^a as well
as the operators \triangle^a and V^a are extended to include the new
anticanonical pairs \pi^{Aa}, \bar{\phi}_A. A new version of the gauge fixing
mechanism in the Lagrangian effective action is proposed. The corresponding
functional integral is shown to be gauge independent.Comment: 7 pages,latexfil
Quantum Sp(2)-antibrackets and open groups
The recently presented quantum antibrackets are generalized to quantum
Sp(2)-antibrackets. For the class of commuting operators there are true quantum
versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a
generalized bracket structure involving higher Sp(2)-antibrackets. It is shown
that these quantum antibrackets may be obtained from generating operators
involving operators in arbitrary involutions. A recently presented quantum
master equation for operators, which was proposed to encode generalized quantum
Maurer-Cartan equations for arbitrary open groups, is generalized to the Sp(2)
formalism. In these new quantum master equations the generalized Sp(2)-brackets
appear naturally.Comment: 17 pages,Latexfile,corrected minor misprint in (78
Gauge theory of second class constraints without extra variables
We show that any theory with second class constraints may be cast into a
gauge theory if one makes use of solutions of the constraints expressed in
terms of the coordinates of the original phase space. We perform a Lagrangian
path integral quantization of the resulting gauge theory and show that the
natural measure follows from a superfield formulation.Comment: 12 pages, Latexfil
Projection operator approach to general constrained systems
We propose a new BRST-like quantization procedure which is applicable to
dynamical systems containing both first and second class constraints. It
requires no explicit separation into first and second class constraints and
therefore no conversion of second class constraints is needed. The basic
ingredient is instead an invariant projection operator which projects out the
maximal subset of constraints in involution. The hope is that the method will
enable a covariant quantization of models for which there is no covariant
separation into first and second class constraints. An example of this type is
given.Comment: 12 pages, Latexfile,minor misprints correcte
Superfield algorithms for topological field theories
A superfield algorithm for master actions of a class of gauge field theories
including topological ones in arbitrary dimensions is presented generalizing a
previous treatment in two dimensions. General forms for master actions in
superspace are given, and possible theories are determined by means of a ghost
number prescription and the master equations. The resulting master actions
determine the original actions together with their gauge invariances.
Generalized Poisson sigma models in arbitrary dimensions are constructed by
means of this algorithm, and other applications in low dimensions are given
including the Chern-Simon model.Comment: 17 pages,Latexfile,minor remarks and change
Open group transformations within the Sp(2)-formalism
Previously we have shown that open groups whose generators are in arbitrary
involutions may be quantized within a ghost extended framework in terms of the
nilpotent BFV-BRST charge operator. Here we show that they may also be
quantized within an Sp(2)-frame in which there are two odd anticommuting
operators called Sp(2)-charges. Previous results for finite open group
transformations are generalized to the Sp(2)-formalism. We show that in order
to define open group transformations on the whole ghost extended space we need
Sp(2)-charges in the nonminimal sector which contains dynamical Lagrange
multipliers. We give an Sp(2)-version of the quantum master equation with
extended Sp(2)-charges and a master charge of a more involved form, which is
proposed to represent the integrability conditions of defining operators of
connection operators and which therefore should encode the generalized quantum
Maurer-Cartan equations for arbitrary open groups. General solutions of this
master equation are given in explicit form. A further extended Sp(2)-formalism
is proposed in which the group parameters are quadrupled to a supersymmetric
set and from which all results may be derived.Comment: 16 pages, Latexfil
Antisymplectic Gauge Theories
A general field-antifield BV formalism for antisymplectic first class
constraints is proposed. It is as general as the corresponding symplectic
BFV-BRST formulation and it is demonstrated to be consistent with a previously
proposed formalism for antisymplectic second class constraints through a
generalized conversion to corresponding first class constraints. Thereby the
basic concept of gauge symmetry is extended to apply to quite a new class of
gauge theories potentially possible to exist.Comment: 13 pages,Latexfile,New introductio
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