Weyl's search for a difference between `physical' and `mathematical' automorphisms

TL;DR

This paper explores Hermann Weyl's lifelong investigation into the differences between physical and mathematical automorphisms, analyzing his ideas in the context of the evolution of gauge theories.

Contribution

It presents Weyl's detailed arguments on the distinction between physical and mathematical automorphisms and contextualizes them within the development of gauge theories.

Findings

Weyl identified key differences in automorphism structures.

His insights influenced the conceptual foundations of gauge theories.

The paper clarifies Weyl's perspective on the epistemic roles of automorphisms.

Abstract

During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.