Gauge Invariance through Gauge Fixing

TL;DR

This paper argues that gauge-fixed descriptions in gauge theory are fundamentally gauge-invariant, highlighting the role of locality and examining the unitary gauge as a notable exception, with implications for understanding physical processes.

Contribution

It challenges the common view that gauge fixing introduces gauge dependence, showing instead that gauge-fixed descriptions are gauge-invariant, especially focusing on locality and the unitary gauge.

Findings

Gauge-fixed descriptions are gauge-invariant representations of physics.

Most gauge-fixed descriptions are non-local, which is the main concern.

The unitary gauge offers a local description, with specific strengths and limitations.

Abstract

Phenomena in gauge theory are often described in the physics literature via a specific choice of gauge. In foundational and philosophical discussions this is often criticized as introducing gauge dependence, and contrasted against (often aspirational) "gauge-invariant" descriptions of the physics. I argue, largely in the context of scalar electrodynamics, that this is misguided, and that descriptions of a physical process within a specific gauge are in fact gauge-invariant descriptions. However, most of them are non-local descriptions of that physics, and I suggest that this ought to be the real objection to such descriptions. I explore the unitary gauge as the exception to this nonlocality and consider its strengths and limitations, as well as (more briefly) its extension beyond scalar electrodynamics.