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

TL;DR

This paper explores the thermodynamics of low-dimensional Bose and Fermi gases using S-matrix formalism and proposes a physical framework related to the Riemann hypothesis, connecting statistical mechanics with number theory.

Contribution

It introduces a novel application of S-matrix formalism to non-relativistic gases in low dimensions and links 1D fermionic systems with the Riemann hypothesis.

Findings

Free energy in 2+1 dimensions expressed via Roger's dilogarithm.

A physical model for understanding the Riemann hypothesis using 1D fermionic gases.

Analogy between relativistic and non-relativistic low-dimensional gases.

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.