Many-Body Fermions and Riemann Hypothesis

TL;DR

This paper explores the algebraic structure of eigenvalues in a many-body fermionic system with a quadratic Hamiltonian and discusses potential connections to the Riemann Hypothesis.

Contribution

It provides an exact analysis of the eigenvalue spectrum of a quadratic fermionic Hamiltonian and investigates its possible links to the Riemann Hypothesis.

Findings

Eigenvalues form an algebraic structure related to non-interacting fermions.

The system's spectrum is exactly constructed using single fermion excitations.

Discussion of potential implications for the Riemann Hypothesis.

Abstract

We study the algebraic structure of the eigenvalues of a Hamiltonian that corresponds to a many-body fermionic system. As the Hamiltonian is quadratic in fermion creation and/or annihilation operators, the system is exactly integrable and the complete single fermion excitation energy spectrum is constructed using the non-interacting fermions that are eigenstates of the quadratic matrix related to the system Hamiltonian. Connection to the Riemann Hypothesis is discussed.