Spectral action in noncommutative geometry: An example

Abstract

This is a report on a joint work [12] with D. Essouabri, C. Levy and A. Sitarz. The spectral action on noncommutative torus is obtained, using a Chamseddine--Connes formula via computations of zeta functions. The importance of a Diophantine condition is outlined as far as the difficulties to go beyond. Some results on holomorphic continuation of series of holomorphic functions are presented.

References in corpus (4)

• Noncommutative Induced Gauge Theory
• Inner fluctuations of the spectral action
• Heat kernel and number theory on NC-torus
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane