Second Quantization and the Spectral Action

Abstract

We consider both the bosonic and fermionic second quantization of spectral triples in the presence of a chemical potential. We show that the von Neumann entropy and the average energy of the Gibbs state defined by the bosonic and fermionic grand partition function can be expressed as spectral actions. It turns out that all spectral action coefficients can be given in terms of the modified Bessel functions. In the fermionic case, we show that the spectral coefficients for the von Neumann entropy, in the limit when the chemical potential $\mu$ approaches $0,$ can be expressed in terms of the Riemann zeta function. This recovers a result of Chamseddine-Connes-van Suijlekom.

Author list is expanded. The calculations in the new version are extended to two more Hamiltonians. New references added

References in corpus (1)

• Spectral Action in Noncommutative Geometry

Cited by in corpus (3)

• A survey of spectral models of gravity coupled to matter
• On multimatrix models motivated by random Noncommutative Geometry I: the Functional Renormalization Group as a flow in the free algebra
• Computing the spectral action for fuzzy geometries: from random noncommutative geometry to bi-tracial multimatrix models