An Approach to the Equivalence Theorem by the Slavnov-Taylor Identities

Abstract

We discus the Equivalence Theorem (ET) in the BRST formalism. In par- ticular the Slavnov-Taylor (ST) identities, derived at the formal level in the path-integral approach, are considered at the quantum level and are shown to be always anomaly free. Some discussion is devoted to the transformation of the flelds; in fact the existence of a local inverse (at least as a formal power expansion) suggests a formulation of the ET, which allows a nilpotent BRST symmetry. This strategy cannot be implemented at the quantum level if the inverse is non-local. In this case we propose an alternative formula- tion of the ET, where, by using Faddeev-Popov flelds, this di-culty is circumvented. In fact this approach allows the loop expansion both in the original and in the transformed theory. In this case the algebraic formulation of the problem can be simplifled by intro- ducing some auxiliary flelds. The auxiliary flelds can be eliminated by using the method of Batalin-Vilkovisky. We study the quantum deformation of the associated ST identity and show that a selected set of Green functions, which in some cases can be identifled with the physical observables of the model, does not depend on the choice of the transformation of the flelds. The computation of the cohomology for the classical linearized ST operator is performed by purely algebraic methods. We do not rely on power-counting arguments. In general the transformation of the flelds yields a non-renormalizable theory. When the equivalence is established between a renormalizable and a non-renormalizable theory, the ET provides a way to give a meaning to the last one by using the resulting ST identity. In this case the Quantum Action Principle cannot be of any help in the discussion of the ET. We assume and discuss the validity of a Quasi Classical Action Principle, which turns out to be su-cient for the present work. As an example we study the renormalizability and unitarity of massive QED in Proca's gauge by starting from a linear Lorentz-covariant gauge.