Polymeric quantum mechanics and the zeros of the Riemann zeta function
arXiv:1610.01957 · doi:10.1142/S0219887818500950
Abstract
We analize the Berry-Keating model and the Sierra and Rodríguez-Laguna Hamiltonian within the polymeric quantization formalism. By using the polymer representation, we obtain for both models, the associated polymeric quantum Hamiltonians and the corresponding stationary wave functions. The self-adjointness condition provide a proper domain for the Hamiltonian operator and the energy spectrum, which turned out to be dependent on an introduced scale parameter. By performing a counting of semiclassical states, we prove that the polymer representation reproduces the smooth part of the Riemann-von Mangoldt formula, and introduces a correction depending on the energy and the scale parameter, which resembles the fluctuation behavior of the Riemann zeros.
16 pages, no figures. Asymptotic analysis of the counting of semiclassical states corrected. Published version
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