Finite field-dependent BRST–anti-BRST transformations: Jacobians and application to the Standard Model

Abstract

We continue our research[Formula: see text] and extend the class of finite BRST–anti-BRST transformations with odd-valued parameters [Formula: see text], [Formula: see text], introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST–anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST–anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST–anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST–anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters [Formula: see text] is obtained, providing the equivalence of path integrals in any 3-parameter [Formula: see text]-like gauges. The Gribov–Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in [Formula: see text]-like gauges, in a gauge-independent way using field-dependent BRST–anti-BRST transformations, and in [Formula: see text]-like gauges using transverse-like non-Abelian gauge fields.