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

TL;DR

This paper explores the Equivalence Theorem within the BRST formalism, proposing an alternative approach using Faddeev-Popov fields to address non-local inverse transformations and studying the associated Slavnov-Taylor identities.

Contribution

It introduces a new formulation of the Equivalence Theorem that circumvents non-local inverse issues using Faddeev-Popov fields and analyzes the quantum deformation of Slavnov-Taylor identities.

Findings

The ST identity remains anomaly free.

Certain Green functions are independent of field transformations.

The approach applies to renormalizable and non-renormalizable theories.

Abstract

We discuss the Equivalence Theorem (ET) in the BRST formalism. The existence of a local inverse of the field transformation (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 formulation of the ET, where, by using Faddeev-Popov fields, this difficulty is circumvented. We study the quantum deformation of the associated ST identity, which turns out to be anomaly free, and show that a selected set of Green functions, which in some cases can be identified with the physical observables of the model, does not depend on the choice of the transformation of the fields. In general the transformation of the fields 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 sufficient 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.