title: Nonclassical degrees of freedom in the Riemann Hamiltonian.
abstract: The Hilbert-Pólya 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 the Altland-Zirnbauer 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.
authors: Department of Physics, University of California, Santa Barbara, California 93106, USA. mark@physics.ucsb.edu
authors: Mark
authors: M
authors: Srednicki