Second quantization and the spectral action

JOURNAL OF GEOMETRY AND PHYSICS

卷:167

Article

Dong, Rui¹  Khalkhali, Masoud²  van Suijlekom, Walter D.¹ 

[1] Radboud Univ Nijmegen, Inst Math Astrophys & Particle Phys, Heyendaalseweg 135, NL-6525 AJ Nijmegen, Netherlands

[2] Univ Western Ontario, Dept Math, London, ON, Canada

关键词: Noncommutative geometry;    Spectral action;    Second quantization;   

DOI  :  10.1016/j.geomphys.2021.104285

来源: Elsevier

【 摘 要 】

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. (C) 2021 The Author(s). Published by Elsevier B.V.

【 授权许可】

Free