Nonclassical Degrees of Freedom in the Riemann Hamiltonian
Mathematical Physics
2015-05-28 v6 math.MP
Number Theory
Chaotic Dynamics
Quantum Physics
Abstract
The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Riemann zeta function are eigenvalues of a quantum hamiltonian. If so, conjectures by Katz and Sarnak put this hamiltonian in Altland and Zirnbauer's universality class C. This implies that the system must have a nonclassical two-valued degree of freedom. In such a system, the dominant primitive periodic orbits contribute to the density of states with a phase factor of -1. This resolves a previously mysterious sign problem with the oscillatory contributions to the density of the Riemann zeros.
Keywords
Cite
@article{arxiv.1105.2342,
title = {Nonclassical Degrees of Freedom in the Riemann Hamiltonian},
author = {Mark Srednicki},
journal= {arXiv preprint arXiv:1105.2342},
year = {2015}
}
Comments
4 pages, no figures; v3-6 have minor corrections to v2, v2 has a more complete solution of the sign problem than v1