The Riemann Zeros as Spectrum and the Riemann Hypothesis

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.