Gauge-invariant matter field actions from iterative N\"other coupling

TL;DR

This paper demonstrates that iterative N"other coupling of matter fields to Abelian gauge fields reproduces the standard non-Abelian gauge invariant actions, offering a non-geometrical perspective on gauge theories.

Contribution

It shows that iterative N"other coupling can generate gauge-invariant matter actions equivalent to those from minimal coupling, extending Deser's work to arbitrary matter representations.

Findings

Iterative N"other coupling reproduces standard gauge-invariant actions.

The method applies to scalar, spinor, and vector fields in any representation.

Provides a non-geometrical approach to gauge theory formulation.

Abstract

Generalizing Deser's work on pure $SU(2)$ gauge theory, we consider scalar, spinor and vector matter fields transforming under arbitrary representations of a non-Abelian, compact, semisimple internal Lie group which is a global symmetry of their actions. These matter fields are coupled to Abelian gauge fields through the process of iterative N\"other coupling. This procedure is shown to yield precisely the same locally gauge invariant theory (with the non-Abelian group as the gauge group) as obtained by the usual minimal coupling prescription originating from the Gauge Principle. Prospects of this non-geometrical formulation, towards better understanding of physical aspects of gauge theories, are briefly discussed.