Finite Field-Dependent BRST Transformations as Quantum Canonical Flows in the Batalin-Vilkovisky Formalism

Abstract

We reformulate finite field-dependent BRST   transformations as quantum canonical flows in the Batalin--Vilkovisky   field-antifield formalism. The starting point is not an ansatz for the Jacobian but a path between two gauge-fixing fermions. The change of gauge is represented by a one-parameter family of BV Lagrangian submanifolds, while a field-dependent BRST transformation is identified with the field-space projection of a canonical flow generated by the gauge-fixed BV master action. This leads to a gauge-fermion transgression equation in which the Jacobian and the variation of the gauge-fixing fermion are two components of one quantum canonical transport law.

For an anomaly-free theory satisfying the quantum master equation, we show that the partition function is independent of the chosen gauge-fixing path. We then apply the construction to non-Abelian Yang-Mills theory and to the reducible Abelian rank-two antisymmetric tensor theory. In the latter case, the complete ghost and ghost-of-ghost hierarchy is incorporated naturally in the BV master action. Covariant/Lorentz and axial gauges appear as two endpoints of a single BV path. We derive a compact compensation condition for finite field-dependent transformations and identify the precise role of the BV Laplacian in the Jacobian. The resulting framework clarifies the relation between FFBRST transformations, gauge-fixing canonical transformations, and the quantum master equation. It also shows why a local Jacobian cannot be assumed in general: locality is a property of the chosen generator and regularization, not of finite field dependence by itself.