Index Theorem in Finite Noncommutative Geometry

TL;DR

This paper formulates an index theorem within finite noncommutative geometry using the Ginsparg-Wilson relation, extends it to broken gauge symmetries, and explores topological aspects in gauge theory.

Contribution

It introduces a finite noncommutative index theorem based on the Ginsparg-Wilson relation and extends it to cases with spontaneous gauge symmetry breaking.

Findings

Index theorem formulated in finite noncommutative geometry.

Extension to spontaneously broken gauge symmetries.

Analysis of topological features in gauge theories.

Abstract

Index theorem is formulated in noncommutative geometry with finite degrees of freedom by using Ginsparg-Wilson relation. It is extended to the case where the gauge symmetry is spontaneously broken. Dynamical analysis about topological aspects in gauge theory is also shown.