The Gauge Argument: A Noether Reason

TL;DR

This paper revisits the gauge argument in physics, reconstructing it as a theorem using Noether's second theorem, to clarify how gauge symmetry constrains physical theories' dynamics.

Contribution

It introduces a more general gauge argument based on Noether's second theorem, offering a clearer understanding of gauge symmetry's role in constraining models.

Findings

Reconstructed the gauge argument as a valid quantum theorem.

Presented a more general gauge argument framework.

Clarified the role of gauge symmetry in constraining dynamics.

Abstract

Why is gauge symmetry so important in modern physics, given that one must eliminate it when interpreting what the theory represents? In this paper we discuss the sense in which gauge symmetry can be fruitfully applied to constrain the space of possible dynamical models in such a way that forces and charges are appropriately coupled. We review the most well-known application of this kind, known as the 'gauge argument' or 'gauge principle', discuss its difficulties, and then reconstruct the gauge argument as a valid theorem in quantum theory. We then present what we take to be a better and more general gauge argument, based on Noether's second theorem in classical Lagrangian field theory, and argue that this provides a more appropriate framework for understanding how gauge symmetry helps to constrain the dynamics of physical theories.