On anomalies and noncommutative geometry

TL;DR

This paper explores how fundamental structures of Connes' noncommutative geometry appear naturally in quantum field theory, highlighting recent collaborative work and providing insights into the intersection of these mathematical and physical frameworks.

Contribution

It demonstrates the emergence of noncommutative geometric structures within quantum field theory, connecting abstract mathematics with physical models.

Findings

Identification of noncommutative geometric structures in quantum field theory

Connection between Connes' geometry and physical models

Insights into the mathematical foundations of quantum physics

Abstract

I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.