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2019

Second Quantization and the Spectral Action

Dong, Rui, Khalkhali, Masoud, van Suijlekom, Walter D.

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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.

Second Quantization and the Spectral Action · Around

Built on

Tables of Integral Transforms: Based, in Part, on Notes Left by Harry Bateman
Bateman Manuscript Project, H. Bateman, A. Erdélyi, and United States Office of Naval Research · 1954
Earlier work this paper cites.
Invariants of the heat equation
H. D. Fegan and P. Gilkey · 1985
Earlier work this paper cites.
Noncommutative Geometry
A. Connes · 1994
Earlier work this paper cites.
Zeta and eta functions for Atiyah–Patodi–Singer operators
G. Grubb and R.T. Seeley · 1996
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