Peter M. Lavrov

A systematic study of finite BRST-BV transformations in field-antifield formalism

We study systematically finite BRST-BV transformations in the field–antifield formalism. We present explicitly their Jacobians and the form of a solution to the compensation equation determining the functional field dependence of finite Fermionic parameters, necessary to generate arbitrary finite change of gauge-fixing functions in the path integral.

A systematic study of finite field-dependent BRST-BV transformations in Sp(2) extended field–antifield formalism

In the framework of Sp(2) extended Lagrangian field–antifield BV formalism, we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generating arbitrary finite change of the gauge-fixing function in the path integral.

A systematic study of finite BRST-BV transformations within W–X formulation of the standard and the Sp(2)-extended field–antifield formalism

Finite BRST-BV transformations are studied systematically within the W–X formulation of the standard and the Sp(2)-extended field–antifield formalism. The finite BRST-BV transformations are introduced by formulating a new version of the Lie equations. The corresponding finite change of the gauge-fixing master action X and the corresponding Ward identity are derived.

Closed description of arbitrariness in resolving quantum master equation

Abstract In the most general case of the Delta exact operator valued generators constructed of an arbitrary Fermion operator, we present a closed solution for the transformed master action in terms of the original master action in the closed form of the corresponding path integral. We show in detail how that path integral reduces to the known result in the case of being the Delta exact generators constructed of an arbitrary Fermion function.

Representation of a gauge field via intrinsic “BRST” operator

Abstract We show that there exists a representation of a matrix-valued gauge field via intrinsic “BRST” operator assigned to matrix-valued generators of a gauge algebra. In this way, we reproduce the standard formulation of the ordinary Yang–Mills theory. In the case of a generating quasigroup/groupoid, we give a natural counterpart to the Yang–Mills action. The latter counterpart does also apply as to the most general case of an involution for matrix-valued gauge generators.

IRREDUCIBLE GAUGE THEORIES IN THE FRAMEWORK OF THE Sp(2)-COVARIANT QUANTIZATION METHOD

Irreducible gauge theories in both the Lagrangian and Hamiltonian versions of the Sp(2)-covariant quantization method are studied. Solutions to generating equations are obtained in the form of expansions in power series of ghost and auxiliary variables up to the third order inclusive.

Legendre transformations and Clairaut-type equations

Abstract It is noted that the Legendre transformations in the standard formulation of quantum field theory have the form of functional Clairaut-type equations. It is shown that in presence of composite fields the Clairaut-type form holds after loop corrections are taken into account. A new solution to the functional Clairaut-type equation appearing in field theories with composite fields is found.

Does the nontrivially deformed field–antifield formalism exist?

We reformulate the Lagrange deformed field-antifield BV -formalism suggested, in terms of the general Euler vector field

Quantum antibrackets: Polarization and parametrization

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Multiplicative renormalization of Yang–Mills theories in the background-field formalism

generated by the antisymplectic potential. That