On the effect of derivative interactions in quantum field theory

TL;DR

This paper investigates how adding total derivatives to interaction terms in quantum field theory affects the theory, providing an all-orders formula to understand these effects beyond perturbative orders.

Contribution

It introduces an all-orders formula to analyze the impact of derivative interactions in quantum field theory, advancing beyond previous perturbative limitations.

Findings

Derived an all-orders formula for derivative interactions

Clarified conditions under which derivatives alter the theory

Supported a quantum consistency approach to particle interactions

Abstract

There exist several good reasons why one may wish to add a total derivative to an interaction in quantum field theory, e.g., in order to improve the perturbative construction. Unlike in classical field theory, adding derivatives in general changes the theory. The analysis whether and how this can be prevented, is presently limited to perturbative orders $g^n$ , $n \leq 3$. We drastically simplify it by an all-orders formula, which also allows to answer some salient structural questions. The method is part of a larger program to (re)derive interactions of particles by quantum consistency conditions, rather than a classical principle of gauge invariance.