Gauges, Holes, and their `Connections'

TL;DR

This paper extends the hole argument to gauge field theories within fiber bundle geometry, challenging substantivalism and advocating for a relational interpretation of gauge fields.

Contribution

It introduces a generalized hole argument for gauge theories in fiber bundles, clarifying the conceptual foundations and challenging substantivalist views.

Findings

Generalized hole argument rules out fiber bundle substantivalism

Supports a relational view of gauge field geometry

Clarifies terminology in gauge field theories

Abstract

The purpose of this paper is to present a generalized hole argument for gauge field theories and their geometrical setting in terms of fiber bundles. The generalized hole argument is motivated and extended from the spacetime hole arguments which appear in spacetime theories based on differentiable manifolds such as general relativity. Analogously, the generalized hole argument rules out fiber bundle substantivalism and, thus, a relationalistic interpretation of the geometry of fiber bundle spaces is favoured. Along the way, the concept of gauge field theories will be analyzed via considering the gauge principle and thereby hopefully clarifying certain terminological ambiguities.