Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis
Mathematical Physics
2008-11-26 v3 Statistical Mechanics
High Energy Physics - Theory
math.MP
Number Theory
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.
Keywords
Cite
@article{arxiv.math-ph/0611043,
title = {Interacting Bose and Fermi gases in low dimensions and the Riemann hypothesis},
author = {André LeClair},
journal= {arXiv preprint arXiv:math-ph/0611043},
year = {2008}
}
Comments
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