Finite BRST–antiBRST transformations in Lagrangian formalism

Abstract

We continue the study of finite BRST–antiBRST transformations for general gauge theories in Lagrangian formalism initiated in [1], with a doublet λa, a=1,2, of anticommuting Grassmann parameters, and find an explicit Jacobian corresponding to this change of variables for constant λa. This makes it possible to derive the Ward identities and their consequences for the generating functional of Green's functions. We announce the form of the Jacobian (proved to be correct in [31]) for finite field-dependent BRST–antiBRST transformations with functionally-dependent parameters, λa=saΛ, induced by a finite even-valued functional Λ(ϕ,π,λ) and by the generators sa of BRST–antiBRST transformations, acting in the space of fields ϕ, antifields ϕa⁎,ϕ¯ and auxiliary variables πa,λ. On the basis of this Jacobian, we present and solve a compensation equation for Λ, which is used to achieve a precise change of the gauge-fixing functional for an arbitrary gauge theory. We derive a new form of the Ward identities, containing the parameters λa, and study the problem of gauge-dependence. The general approach is exemplified by the Freedman–Townsend model of a non-Abelian antisymmetric tensor field.