On Gauge Invariance and Minimal Coupling

TL;DR

This paper critically examines the concept of minimal coupling in gauge theories, demonstrating its ill-defined nature and highlighting misconceptions in Higgs boson interaction analyses, especially in strongly coupled gauge theories.

Contribution

It challenges the widespread use of minimal coupling as a fundamental principle, providing pedagogical examples and clarifying misconceptions in gauge theory dynamics.

Findings

Minimal coupling is ill-defined in field theory and quantum mechanics.

Many arguments in Higgs boson interaction literature are flawed due to reliance on minimal coupling.

Clarification of misconceptions about strongly coupled gauge theories.

Abstract

The principle of minimal coupling has been used in the study of Higgs boson interactions to argue that certain higher dimensional operators in the low-energy effective theory generalization of the Standard Model are suppressed by loop factors, and thus smaller than others. It also has been extensively used to analyze beyond-the-standard-model theories. We show that in field theory, and even in quantum mechanics, the concept of minimal coupling is ill-defined and inapplicable as a general principle, and give many pedagogical examples which illustrate this fact. We also clarify some related misconceptions about the dynamics of strongly coupled gauge theories. Many arguments in the literature on Higgs boson interactions that use minimal coupling, particularly in pseudo-Goldstone Higgs theories, are inherently flawed.