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arXiv · 1105.2342

Nonclassical Degrees of Freedom in the Riemann Hamiltonian

Mark Srednicki
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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.

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Mark Srednicki. 2011-11-14. Nonclassical Degrees of Freedom in the Riemann Hamiltonian. https://doi.org/10.1103/physrevlett.107.100201

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