Quantum Field Theory and Differential Geometry

TL;DR

This paper explores how topological Yang-Mills theory, originating from physics, serves as a powerful tool for studying differential geometry, highlighting the evolving relationship between physics and mathematics.

Contribution

It introduces the use of physical theories, specifically topological Yang-Mills theory, as novel methods for investigating differential geometric structures.

Findings

Physics-inspired methods provide new insights into differential geometry

The interplay between physics and mathematics has entered a new stage

Topological Yang-Mills theory offers a unique perspective on geometric problems

Abstract

We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize that this phenomenon demonstrates that the interrelation between physics and mathematics have come into a new stage.