The Riemann Zeta Function and Vacuum Spectrum

TL;DR

This paper proposes a novel spectral interpretation of the Riemann zeta function by linking its zeros to poles of the S matrix in a quantum vacuum model, aligning with random matrix theory.

Contribution

It introduces a new approach focusing on S matrix poles rather than self-adjoint operators to interpret the Riemann zeros.

Findings

Resonance distribution matches random matrix theory predictions.

The model links Riemann zeros to virtual resonances in a quantum vacuum.

Provides a new perspective on the spectral interpretation of the zeta function.

Abstract

A variant for the Hilbert and Polya spectral interpretation of the Riemann zeta function is proposed. Instead of looking for a self-adjoint linear operator H, whose spectrum coincides with the Riemann zeta zeros, we look for the complex poles of the S matrix that are mapped into the critical line in coincidence with the nontrivial Riemann zeroes. The associated quantum system, an infinity of "virtual resonances" described by the corresponding S matrix poles, can be interpreted as the quantum vacuum. The distribution of energy levels differences associated to these resonances shows the same characteristic features of random matrix theory.