Abstract
A Hamiltonian operator is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of is , which is consistent with the Berry-Keating conjecture. While is not Hermitian in the conventional sense, is symmetric with a broken symmetry, thus allowing for the possibility that all eigenvalues of are real. A heuristic analysis is presented for the construction of the metric operator to define an inner-product space, on which the Hamiltonian is Hermitian. If the analysis presented here can be made rigorous to show that is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true.
- Received 23 September 2016
DOI:https://doi.org/10.1103/PhysRevLett.118.130201
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society