Defining geometric gauge theory to accommodate particles, continua, and fields

TL;DR

This paper develops a generalized geometric gauge theory framework that unifies classical electromagnetism, gravity, and matter fields, providing new insights and consistent formulations for these fundamental physical models.

Contribution

It formalizes and extends geometric gauge theory, introducing a unified approach applicable to classical electromagnetism, gravity, and matter fields with improved Lagrangians and interpretations.

Findings

Derived a gauge-independent Galilean Lagrangian.

Provided a geometric interpretation of metric dependence of four-momentum.

Developed a gauge theory of gravity including matter fields.

Abstract

Gauge theory underpins the quantum field theories of the standard model, and in a previous paper was shown via a geometric approach to describe classical electromagnetism in a form which approximates QED. Here we formalize and generalize the notion of a geometric gauge theory, then apply this framework to classical physical models, including an improved Lagrangian for matter field electromagnetism. We find a remarkably consistent series of actions, with straightforward limits under which each previous one may be obtained. Ancillary benefits include a gauge-independent Galilean Lagrangian, a geometric interpretation for the unusual metric dependence of four-momentum, a modern treatment of the effects of worldline variation on the four-current, a gauge theory of gravity which includes a matter field, and consistent units for matter field electromagnetism.