Euler and Pontryagin currents of the Dirac operator

TL;DR

This paper explores how Euler and Pontryagin currents on spin manifolds relate to the Dirac operator, linking geometric and topological concepts to quantum matter dynamics.

Contribution

It introduces a novel way to express topological currents using tensors associated with the Dirac equation on spin manifolds.

Findings

Euler and Pontryagin currents can be expressed in terms of Dirac-related tensors

The approach connects geometric topology with quantum matter dynamics

Provides a framework for analyzing topological effects in quantum field theories

Abstract

On differential manifolds with spinor structure, it is possible to express the Euler and Pontryagin currents in terms of tensors that also appear as source in the Dirac equation. It is hence possible to tie concepts rooted in geometry and topology to dynamical characters of quantum matter.