The Riemann zeros as spectrum and the Riemann hypothesis

TL;DR

This paper models the Riemann zeros as spectral bound states of a Dirac fermion in Rindler spacetime with delta potentials, proposing a potential proof of the Riemann hypothesis and an experimental observation method.

Contribution

It introduces a novel spectral model linking Riemann zeros to a Dirac fermion system with delta potentials, offering a new approach to the Riemann hypothesis.

Findings

Riemann zeros correspond to bound states in the model

Self-adjoint extension tuned to zeta function phase

Proposes an interferometer for experimental observation

Abstract

We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers. The corresponding Hamiltonian admits a self-adjoint extension that is tuned to the phase of the zeta function, on the critical line, in order to obtain the Riemann zeros as bound states. The model suggests a proof of the Riemann hypothesis in the limit where the potentials vanish. Finally, we propose an interferometer that may yield an experimental observation of the Riemann zeros.