Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis

Abstract

We apply the S-matrix based finite temperature formalism to non-relativistic Bose and Fermi gases in 1+1 and 2+1 dimensions. In the 2+1 dimensional case, the free energy is given in terms of Roger's dilogarithm in a way analagous to the relativistic 1+1 dimensional case. The 1d fermionic case with a quasi-periodic 2-body potential provides a physical framework for understanding the Riemann hypothesis.

version 3: additional appendix explains how the $\nu$ to $1-\nu$ duality of Riemann's $\zeta (\nu )$ follows from a special modular transformation in a massless relativistic theory

References in corpus (1)

• Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes

Cited by in corpus (2)

• H = x p with interaction and the Riemann zeros
• On the Quantum Reconstruction of the Riemann zeros