arXiv subjects

Igor Batalin

Publications and source records attributed to Igor Batalin.

18 recordsLinked to original sources

arXiv2006

BRST-Invariant Constraint Algebra in Terms of Commutators and Quantum Antibrackets

General structure of BRST-invariant constraint algebra is established, in its commutator and antibracket forms, by means of formulation of algebra-generating equations in yet more extended phase space. New ghost-type variables behave as fields and antifields with respect to quantum antibrackets. Explicit form of BRST-invariant gauge algebra is given in detail for rank-one theories with Weyl- and Wick- ordered ghost sector. A gauge-fixed unitarizing Hamiltonian is constructed, and the formalism is shown to be physically equivalent to the standard BRST-BFV approach.

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arXiv2005

Non-Abelian Conversion and Quantization of Non-scalar Second-Class Constraints

We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The covariance of the construction with respect to the change of the constraint basis is provided by introducing a connection in the ``constraint bundle'', which becomes a key ingredient of the conversion procedure for the non-scalar constraints. Unlike in the case of scalar second-class constraints, no Abelian conversion is possible in general. Within the BRST framework, a systematic procedure is worked out for converting non-scalar second-class constraints into non-Abelian first-class ones. The BRST-extended system is quantized, yielding an explicitly covariant quantization of the original system. An important feature of second-class systems with non-scalar constraints is that the appropriately generalized Dirac bracket satisfies the Jacobi identity only on the constraint surface. At the quantum level, this results in a weakly associative star-product on the phase space.

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arXiv2003

On the transformations of hamiltonian gauge algebra under rotations of constraints

By explicit calculation of the effect of a ghost-dependent canonical transformation of BRST-charge, we derive the corresponding transformation law for structure coefficients of hamiltonian gauge algebra under rotation of constraints.We show the transformation law to deviate from the behaviour (expected naively) characteristic to a genuine connection.

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arXiv2002

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.

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arXiv2001

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.

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arXiv2001

Generalized Poisson sigma models

A general master action in terms of superfields is given which generates generalized Poisson sigma models by means of a natural ghost number prescription. The simplest representation is the sigma model considered by Cattaneo and Felder. For Dirac brackets considerably more general models are generated.

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arXiv2001

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.

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arXiv1999

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.

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arXiv1999

Open group transformations

Open groups whose generators are in arbitrary involutions may be quantized within a ghost extended framework in terms of a nilpotent BFV-BRST charge operator. Previously we have shown that generalized quantum Maurer-Cartan equations for arbitrary open groups may be extracted from the quantum connection operators and that they also follow from a simple quantum master equation involving an extended nilpotent BFV-BRST charge and a master charge. Here we give further details of these results. In addition we establish the general structure of the solutions of the quantum master equation. We also construct an extended formulation whose properties are determined by the extended BRST charge in the master equation.

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arXiv1999

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.

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arXiv1999

General quantum antibrackets

The recently introduced quantum antibracket is further generalized allowing for the defining odd operator Q to be arbitrary. We give exact formulas for higher quantum antibrackets of arbitrary orders and their generalized Jacobi identities. Their applications to BV-quantization and BFV-BRST quantization are then reviewed including some new aspects.

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arXiv1999

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 Δ-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.

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arXiv1998

Dualities between Poisson brackets and antibrackets

Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher Poisson brackets where the latter are of a new type. We give generating functions for these brackets for functions in arbitrary involutions in the original bracket. We also give master equations for generalized Maurer-Cartan equations. The presentation is completely symmetric with respect to Poisson brackets and antibrackets.

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arXiv1998

Open groups of constraints - Integrating arbitrary involutions

A new type of quantum master equation is presented which is expressed in terms of a recently introduced quantum antibracket. The equation involves only two operators: an extended nilpotent BFV-BRST charge and an extended ghost charge. It is proposed to determine the generalized quantum Maurer-Cartan equations for arbitrary open groups. These groups are the integration of constraints in arbitrary involutions. The only condition for this is that the constraint operators may be embedded in an odd nilpotent operator, the BFV-BRST charge. The proposal is verified at the quasigroup level. The integration formulas are also used to construct a generating operator for quantum antibrackets of operators in arbitrary involutions.

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arXiv1997

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.

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arXiv1996

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.

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arXiv1995

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 π^{Aa}. The antibrackets (F, G)^a as well as the operators \triangle^a and V^a are extended to include the new anticanonical pairs π^{Aa}, \barϕ_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.

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arXiv1995

Solving general gauge theories on inner product spaces

By means of a generalized quartet mechanism we show in a model independent way that a BRST quantization on an inner product space leads to physical states of the form |ph>=e^{[Q, ψ]} |ph>_0 where Q is the nilpotent BRST operator, ψa hermitian fermionic gauge fixing operator, and |ph>_0 BRST invariant states determined by a hermitian set of BRST doublets in involution. |ph>_0 does not belong to an inner product space although |ph> does. Since the BRST quartets are split into two sets of hermitian BRST doublets there are two choices for |ph>_0 and the corresponding ψ. When applied to general, both irreducible and reducible, gauge theories of arbitrary rank within the BFV formulation we find that |ph>_0 are trivial BRST invariant states which only depend on the matter variables for one set of solutions, and for the other set |ph>_0 are solutions of a Dirac quantization. This generalizes previous Lie group solutions obtained by means of a bigrading.

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