Cyril Levy (Marseille):

Spectral Action on Noncommutative Torus

Abstract:

A approach of noncommutative quantum field theory is provided by noncommutative geometry throughout the notions of spectral triple and spectral action. After an introduction of the torus as a spectral triple we show how the spectral action on noncommutative torus with charge conjugaison can be obtained, using a Chamseddine--Connes formula, via computations of residues of  ζ functions. The importance of a Diophantine condition on the matrix deformation is outlined. Several results on holomorphic continuation of series of holomorphic functions are obtained in this context.

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