Index Theorem in Finite Noncommutative Geometry

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.

Comments: Latex 4 pages, uses ptptex.cls, Based on talk given at 21st Nishinomiya-Yukawa Memorial Symposium on Theoretical Physics: Noncommutative Geometry and Quantum Spacetime in Physics, Japan, 11-15 Nov 2006