abstract

• We analyze 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 provides 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 also introduces a correction depending on the energy and the scale parameter. This may shed some light on the understanding of the fluctuation behavior of the zeros of the Riemann function from a purely quantum point of view. © 2018 World Scientific Publishing Company.

authors

• Berra Montiel Oscar Jasel
• Molgado Ramos Alberto

publication date

• 2018-01-01

funding provided via

• CB-2014-243433, CB-2017-283838  Grant

published in

• International Journal of Geometric Methods in Modern Physics  Journal

keywords

• Hamiltonian system; Polymeric quantization; Riemann zeta function; self-adjoint extension

Digital Object Identifier (DOI)

• 10.1142/S0219887818500950

start page

end page

volume

• 15

issue

• 6