We consider infinitesimal field-dependent BRS transformations. We show that they can be integrated to yield finite BRS field-dependent transformations and have the same BRS form. We discuss a number of applications of the latter. We show that for certain special field-dependent BRS parameters (evaluated in a closed form), these can be used to connect the Faddeev-Popov effective action in a linear gauge with a gauge parameter λ to (i) the most general BRS–anti-BRS symmetric action in linear gauges, (ii) the Faddeev-Popov effective action in quadratic gauges, and (iii) the Faddeev-Popov effective action with another distinct gauge parameter λ’. In each case, the extra terms in the latter action are shown to arise from the Jacobian for the nonlocal field-dependent BRS transformations. Some applications of these ideas are suggested.

We develop the off-shell nilpotent finite field dependent Becchi–Rouet–Stora–Tyutin (BRST) transformations and show that for different choices of the finite field dependent parameter these transformations connect the generating functionals corresponding to different effective theories. We also construct both on-shell and off-shell finite field dependent anti-BRST transformations for Yang–Mills theories and show that these transformations play the similar role in connecting different generating functionals of different effective theories. Analogous to the finite field dependent BRST transformations, the nontrivial Jacobians of the path integral measure which arise due to the finite field dependent anti-BRST transformations are responsible for the new results. We consider several explicit examples in each case to demonstrate the results.