Field redefinition invariant Lagrange multiplier formalism with gauge symmetries

It has been shown that by using a Lagrange multiplier field to ensure that the classical equations of motion are satisfied, radiative effects beyond one-loop order are eliminated. It has also been shown that through the contribution of some additional ghost fields, the effective action becomes form invariant under a redefinition of field variables, and furthermore, the usual one-loop results coincide with the quantum corrections obtained from this effective action. In this paper, we consider the consequences of a gauge invariance being present in the classical action. The resulting gauge transformations for the Lagrange multiplier field as well as for the additional ghost fields are found. These gauge transformations result in a set of Faddeev-Popov ghost fields arising in the effective action. If the gauge algebra is closed, we find the Becci-Rouet-Stora-Tyutin (BRST) transformations that leave the effective action invariant.