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.

arXiv commentversion 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 (5)

• Bosonic-type S-Matrix, Vacuum Instability and CDD Ambiguities
• Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model
• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• One Dimensional Gas of Bosons with Feshbach Resonant Interactions
• Quantum statistical mechanics of gases in terms of dynamical filling fractions and scattering amplitudes

Cited by in corpus (11)

• Physics of the Riemann Hypothesis
• H = x p with interaction and the Riemann zeros
• Critical point of the two-dimensional Bose gas: an S-matrix approach
• Scrutinizing the Cosmological Constant Problem and a possible resolution
• The Riemann zeros as spectrum and the Riemann hypothesis
• Transcendental equations satisfied by the individual zeros of Riemann $\zeta$, Dirichlet and modular $L$-functions
• S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case
• Statistical and other properties of Riemann zeros based on an explicit equation for the $n$-th zero on the critical line
• An electrostatic depiction of the validity of the Riemann Hypothesis and a formula for the N-th zero at large N
• On the Quantum Reconstruction of the Riemann zeros
• S-matrix approach to quantum gases in the unitary limit I: the two-dimensional case