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Dive into the research topics where I. A. Batalin is active.

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Featured researches published by I. A. Batalin.


Physics Letters B | 1981

Gauge Algebra and Quantization

I. A. Batalin; G. A. Vilkovisky

In the past people believed that if a field action is invariant under some transformations, then these transformations form a Lie group (infinite-dimensional in the case of gauge transformations). But this does not follow from anywhere. In fact the infinitesimal transformations of supergravity form at least apparently an open algebra. Therefore the wish arises to analyse the general situation. This is the purpose of the present work.


Physics Letters B | 1983

A Generalized Canonical Formalism and Quantization of Reducible Gauge Theories

I. A. Batalin; E.S. Fradkin

Abstract A general solution for the S -matrix of relativistic dynamical systems subject to Bose and Fermi first and second class constraints is obtained by canonical quantization in the case of reducibility, i.e. when the first class constraints are linearly dependent. The null-eigenvectors of the constraints may also be linearly dependent and possess null-eigenvectors of their own, which, in their turn, may be linearly dependent, etc. The solution obtained remains valid in the present case of multistage reducibility of constraints.


Physics Letters B | 1983

Feynman rules for reducible gauge theories

I. A. Batalin; G.A. Vilkovisky

Abstract Feynman rules are obtained in the universal way for any gauge theory with linearly dependent generators. The most general prescriptions for gauge fixing are given. The ghost lagrangian is constructed in the case of gauge algebra which is both reducible and open.


Journal of Mathematical Physics | 1990

Covariant quantization of gauge theories in the framework of extended BRST symmetry

I. A. Batalin; P. M. Lavrov; I. V. Tyutin

The quantization rules for gauge theories in the Lagrangian formalism are formulated on the basis of the requirement of an extended BRST symmetry. The independence of the S matrix to the choice of a gauge is proved. The Ward identities are derived, and the existence theorem for the solutions of the generating equations within the given formalism is proved. Rank 1 gauge theories are considered as an example.


Physics Letters B | 1986

Operator Quantization of Dynamical Systems With Irreducible First and Second Class Constraints

I. A. Batalin; E.S. Fradkin

Abstract An operator version is suggested of the generalized canonical quantization method of dynamical systems subjected to irreducible first- and second-class constraints. An operator analog of classical Dirac brackets is realized. Generating equations for the generalized algebra of first- and second-class constraints, as well as for the unitarizing hamiltonian are formulated. In the first-class constraint sector new generating equations are presented directly in terms of operator Dirac brackets.


Journal of Mathematical Physics | 1991

An Sp(2)‐covariant quantization of gauge theories with linearly dependent generators

I. A. Batalin; P. M. Lavrov; I. V. Tyutin

The Sp(2)‐symmetric version of covariant quantization is formulated for the general case of any stage‐reducible gauge theories.


Physics Letters B | 1983

Operator quantization of relativistic dynamical systems subject to first class constraints

I. A. Batalin; E.S. Fradkin

Abstract The operator quantization is carried out of relativistic dynamical systems subjected to first class bosonic and fermionic constraints that generate an open any-rank irreducible gauge algebra.


Journal of Mathematical Physics | 1991

Remarks on the Sp(2)‐covariant Lagrangian quantization of gauge theories

I. A. Batalin; P. M. Lavrov; I. V. Tyutin

The existence of a solution of the exact generating equations (with ℏ≠0) for the Sp(2)‐covariant Lagrangian quantization scheme is established. The characteristic arbitrariness of this solution is also studied. The equivalence between the Sp(2)‐covariant quantization and the standard one is proven.


Journal of Mathematical Physics | 1990

Extended BRST quantization of gauge theories in the generalized canonical formalism

I. A. Batalin; P. M. Lavrov; I. V. Tyutin

The rules of canonical quantization of gauge theories are formulated on the basis of the extended BRST symmetry principle. The existence of solutions of the generating equations of the gauge algebra is proved. Equivalence between the extended BRST quantization and the standard method of generalized canonical quantization is established. Ward identities corresponding to invariance of a theory under the extended BRST symmetry are obtained.


Journal of Mathematical Physics | 1990

An Sp(2)‐covariant version of generalized canonical quantization of dynamical systems with linearly dependent constraints

I. A. Batalin; P. M. Lavrov; I. V. Tyutin

An Sp(2)‐covariant version of the method of generalized canonical quantization of dynamical systems with linearly dependent first‐class constraints is proposed. The existence theorem for solutions of generating equations of a gauge algebra is proved and the natural arbitrariness in these solutions is described. The scheme proposed is shown to be equivalent to the standard version of generalized canonical quantization.

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I. V. Tyutin

Lebedev Physical Institute

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Peter M. Lavrov

Tomsk State Pedagogical University

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E.S. Fradkin

Lebedev Physical Institute

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A. V. Gurevich

Russian Academy of Sciences

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I.V. Tyutin

Lebedev Physical Institute

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Vladimir I. Ritus

Russian Academy of Sciences

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A. M. Semikhatov

Lebedev Physical Institute

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