Gauge field theory without groups

TL;DR

This paper presents a novel approach to gauge field theory that minimizes the importance of groups, emphasizing differential geometry to clarify foundational concepts in the field.

Contribution

It introduces an original perspective that reduces the centrality of groups in gauge theories, aiming to clarify foundational issues through differential geometry.

Findings

Groups are shown to be secondary in gauge theories.

A differential geometric framework clarifies foundational matters.

The approach unifies ideas from previous works and a recent book.

Abstract

Non-standard topics underlying a partly original approach to gauge field theory are concisely introduced, expressing ideas that were broached in several papers and, eventually, exposed in an organized form in a recently published book. By proposing a change of perspective about the roles and relative importance of several notions, this approach seeks to obtain an overall clarification of foundational matters. In particular, by consistently relying on natural differential geometry, the role of groups is shown to be downgradable to secondary.