Prime numbers, atomic nuclei, symmetries and superconductivity

Abstract

The distribution of prime numbers is directly related to the statistical distribution of the nontrivial zeros of the Riemann Zeta function that closely resembles that of energy levels of atomic nuclei. Moreover, Riemann Zeta function plays a fundamental role in many areas of mathematics, from number theory to geometry and theory of dynamical systems and in physics from quantum chaos to the theory of quantum fields and of quasicrystals. Unfortunately, no proof exists of the so-called Riemann hypothesis stating that all its nontrivial zeros lie on the critical line ℜ(s) = ½. A new method is proposed to prove the Riemann hypothesis based on the Hilbert–Polya conjecture and a superconducting-type Hamiltonian in the Hilbert-Fock L2 space.