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Igor A. Batalin

Publications and source records attributed to Igor A. Batalin.

33 records · Page 2Linked to original sources
arXiv2016

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.

hep-th↗
arXiv2015

Finite BRST-BFV transformations for dynamical systems with second-class constraints

We study finite field dependent BRST-BFV transformations for dynamical systems with first- and second-class constraints within the generalized Hamiltonian formalism. We find explicitly their Jacobians and the form of a solution to the compensation equation necessary for generating an arbitrary finite change of gauge-fixing functionals in the path integral.

hep-th↗
arXiv2015

Finite anticanonical transformations in field-antifield formalism

We study the role of arbitrary (finite) anticanonical transformations in the field-antifield formalism, and the gauge-fixing procedure based on the use of these transformations. The properties of the generating functionals of the Green functions subjected to finite anticanonical transformations are considered.

hep-th↗
arXiv2014

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.

hep-th↗
arXiv2014

External Sources in Field-Antifield Formalism

We introduce external sources J_A directly into the quantum master action W of the field-antifield formalism instead of the effective action. The external sources J_A lead to a set of BRST-invariant functions W^A that are in antisymplectic involution. As a byproduct, we encounter quasi--groups with open gauge algebras.

hep-th↗
arXiv2012

A Triplectic Bi-Darboux Theorem and Para-Hypercomplex Geometry

We provide necessary and sufficient conditions for a bi-Darboux Theorem on triplectic manifolds. Here triplectic manifolds are manifolds equipped with two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with ranks equal to 2/3 of the manifold dimension. By definition bi-Darboux coordinates are common Darboux coordinates for two Poisson brackets. We discuss both the Grassmann-even and the Grassmann-odd Poisson bracket case. Odd triplectic manifolds are, e.g., relevant for Sp(2)-symmetric field-antifield formulation. We demonstrate a one-to-one correspondence between triplectic manifolds and para-hypercomplex manifolds. Existence of bi-Darboux coordinates on the triplectic side of the correspondence translates into a flat Obata connection on the para-hypercomplex side.

math-ph↗
arXiv2009

Remarks on Existence of Proper Action for Reducible Gauge Theories

In the field-antifield formalism, we review existence and uniqueness proofs for the proper action in the reducible case. We give two new existence proofs based on two resolution degrees called "reduced antifield number" and "shifted antifield number", respectively. In particular, we show that for every choice of gauge generators and their higher stage counterparts, there exists a proper action that implements them at the quadratic order in the auxiliary variables.

hep-th↗
arXiv2009

A Comparative Study of Laplacians and Schroedinger-Lichnerowicz-Weitzenboeck Identities in Riemannian and Antisymplectic Geometry

We introduce an antisymplectic Dirac operator and antisymplectic gamma matrices. We explore similarities between, on one hand, the Schroedinger-Lichnerowicz formula for spinor bundles in Riemannian spin geometry, which contains a zeroth-order term proportional to the Levi-Civita scalar curvature, and, on the other hand, the nilpotent, Grassmann-odd, second-order Δoperator in antisymplectic geometry, which in general has a zeroth-order term proportional to the odd scalar curvature of an arbitrary antisymplectic and torsionfree connection that is compatible with the measure density. Finally, we discuss the close relationship with the two-loop scalar curvature term in the quantum Hamiltonian for a particle in a curved Riemannian space.

hep-th↗
arXiv2008

Odd Scalar Curvature in Anti-Poisson Geometry

Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure ρif a zero-order term ν_ρ is added to the Δoperator. The effects of this odd scalar term ν_ρ become relevant at two-loop order. We prove that ν_ρ is essentially the odd scalar curvature of an arbitrary torsion-free connection that is compatible with both the anti-Poisson structure E and the density ρ. This extends a previous result for non-degenerate antisymplectic manifolds to degenerate anti-Poisson manifolds that admit a compatible two-form.

hep-th↗
arXiv2008

Odd Scalar Curvature in Field-Antifield Formalism

We consider the possibility of adding a Grassmann-odd function νto the odd Laplacian. Requiring the total Δoperator to be nilpotent leads to a differential condition for ν, which is integrable. It turns out that the odd function νis not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density ρ. The main impact of introducing the νterm is that it makes compatibility relations between E and ρobsolete. We give a geometric interpretation of νas (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and ρ-compatible connection. We show that the total Δoperator is a ρ-dressed version of Khudaverdian's Δ_E operator, which takes semidensities to semidensities. We also show that the construction generalizes to the situation where ρis replaced by a non-flat line bundle connection F. This generalization is implemented by breaking the nilpotency of Δwith an arbitrary Grassmann-even second-order operator source.

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