On Generalized Gauge-Fixing in the Field-Antifield Formalism

TL;DR

This paper explores a highly general covariant gauge-fixing approach within the field-antifield formalism, analyzing reducible gauge-fixing algebras and their measure contributions, extending to multi-level structures.

Contribution

It introduces a comprehensive framework for reducible gauge-fixing algebras and their measure contributions, generalizing to arbitrary stages and multi-level structures within the formalism.

Findings

Detailed treatment of first-stage reducible gauge-fixing algebra

Derivation of measure contributions from first principles

Extension to W-X alternating multi-level structures

Abstract

We consider the problem of covariant gauge-fixing in the most general setting of the field-antifield formalism, where the action W and the gauge-fixing part X enter symmetrically and both satisfy the Quantum Master Equation. Analogous to the gauge-generating algebra of the action W, we analyze the possibility of having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing algebra of the so-called first-stage in full detail and generalize to arbitrary stages. The associated "square root" measure contributions are worked out from first principles, with or without the presence of antisymplectic second-class constraints. Finally, we consider an W-X alternating multi-level generalization.