Abstract :
Following our recent works [S. Joffily, Jost function, prime numbers and Riemann zeta function, Contribution to Roberto Salmeron Festschrift, eds. by R. Aldrovandi, et al., AIAFEX, Rio de Janeiro, 2003, math-ph/0303014, S. Joffily, “The Riemann Zeta Function and Vacuum Spectrum”, Proceedings of Science, PoS (WC2004) 026, hep-th/0412217] where it was suggested a “potential scattering” Hilbert-Polya conjecture, such that the nontrivial zeros of Riemannʹs zeta function could be put in one-to-one correspondence with the zeros of the s-wave Jost function for finite range potentials in the complex momenta plane, we extend our investigation to a relativistic S matrix for a Dirac particle scattering. We then present a description of the vacuum structure as being a dynamical system described by “virtual resonances”, completely independent of the second quantization.
