Motivating Gauge-Invariant Approaches to Particle Physics

TL;DR

This paper advocates for the importance of gauge-invariant approaches in particle physics, emphasizing their conceptual clarity and consistency with mathematical theorems that challenge standard methods.

Contribution

It argues for increased focus on gauge-invariant formulations, highlighting their advantages in resolving theoretical issues and aligning with the mathematical framework.

Findings

Gauge-invariant approaches avoid problems posed by Elitzur's theorem, Gribov ambiguity, and Haag's theorem.

Standard approaches use non-gauge-invariant fields which are not physically real.

Gauge-invariant reformulations improve conceptual and mathematical consistency in particle physics.

Abstract

There is noticeable consensus among physicists and philosophers that only gauge-invariant quantities can be physically real. However, this insight that physical quantities must be gauge-invariant is not well-reflected in standard approaches to particle physics. For instance, each and every elementary field/particle of the Standard Model fails to be gauge-invariant! The main objective of this paper is to offer an accessible, concise, and convincing analysis of why philosophers and physicists should devote more of their energy to working on gauge-invariant approaches. Correspondingly, the thesis of this paper is that pursuing gauge-invariant approaches has several virtues. For instance, gauge-invariant reformulations allow us to make particle physics consistent with the mathematical framework in which it is formulated. This is illustrated by how mathematical theorems such as Elitzur's theorem, the Gribov ambiguity, and Haag's theorem pose problems for standard approaches but are avoided by gauge-invariant approaches.