Self-Interaction and Gauge Invariance

TL;DR

This paper presents a unified derivation of the nonlinearities in Einstein, Yang-Mills, and meson systems, showing they are dictated by gauge invariance and conserved currents, using a first-order formalism.

Contribution

It provides a simple, unified closed-form derivation of gauge-invariant nonlinearities across multiple fundamental theories, highlighting their origin from conserved currents.

Findings

Non-linearities are required by locality and consistency.

Non-linearities are determined by conserved currents.

First-order formalism yields a simple cubic self-interaction.

Abstract

A simple unified closed form derivation of the non-linearities of the Einstein, Yang-Mills and spinless (e.g., chiral) meson systems is given. For the first two, the non-linearities are required by locality and consistency; in all cases, they are determined by the conserved currents associated with the initial (linear) gauge invariance of the first kind. Use of first-order formalism leads uniformly to a simple cubic self-interaction.