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The Riemann Zeta Function and Vacuum Spectrum

S. Joffily
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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.

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S. Joffily. 2004-12-18. The Riemann Zeta Function and Vacuum Spectrum. https://arxiv.org/abs/hep-th/0412217

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