The Equivalence Theorem in Effective Theories

TL;DR

This paper revisits the equivalence theorem within quantum effective theories, introducing modifications and a graph-based proof to clarify the cancellation of contributions in Green function calculations.

Contribution

It provides a modified formulation of the equivalence theorem applicable to quantum effective theories and offers a graph-based proof method.

Findings

The modified theorem applies to quantum infinite-component effective theories.

Graphical methods reveal mutual cancellations in Green function contributions.

The approach enhances understanding of equivalence in quantum field theories.

Abstract

The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancelation of different groups of contributions.