Physics NotePublished
The Riemann Zeta Function and Vacuum Spectrum
Sérgio Joffily
2004
Publication details
- Authors
- Sérgio Joffily
- Type
- Physics Note
- Status
- Published
- Publication date
- 2004
- Description
- 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.
- Year
- 2004
- Number
- CBPF-NF-035/04
- Linked to a thesis
- No
- Linked to a grant
- No