Once again on the equivalence theorem

TL;DR

This paper proves the equivalence theorem in quantum field theory using the field-antifield formalism, illustrating how different finite counterterms can lead to non-equivalent quantum theories while the theorem still holds.

Contribution

It provides a proof of the equivalence theorem within the field-antifield formalism and discusses its implications for different choices of counterterms.

Findings

The equivalence theorem remains valid despite different counterterm choices.

Different finite counterterms can produce non-equivalent quantum theories.

The proof is demonstrated through a specific model example.

Abstract

We present the proof of the equivalence theorem in quantum field theory which is based on a formulation of this problem in the field-antifield formalism. As an example, we consider a model in which a different choices of natural finite counterterms is possible, leading to physically non-equivalent quantum theories while the equivalent theorem remains valid.