Supersymmetric quantum mechanics and the Riemann hypothesis

TL;DR

This paper introduces a supersymmetric quantum mechanical model where the energy levels are linked to the Riemann zeta function, connecting zeros of the zeta function to ground state energies, offering a novel physical perspective on the Riemann hypothesis.

Contribution

It constructs a supersymmetric quantum model with energy eigenvalues related to the Riemann zeta function, providing a new framework to study its zeros.

Findings

Zeros of the zeta function correspond to zero ground state energies

The model establishes a natural form of supersymmetry related to the zeta function

Provides a physical analogy for the distribution of zeta zeros

Abstract

We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally correspond to the vanishing ground state energies in this model. The model provides a natural form of supersymmetry.