期刊
PHYSICAL REVIEW LETTERS
卷 118, 期 13, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.118.130201
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资金
- Russian Science Foundation [16-11-10218]
- Canada Research Chairs program
- Government of Canada through Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Research, Innovation and Science
- Russian Science Foundation [16-11-10218] Funding Source: Russian Science Foundation
A Hamiltonian operator H 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 H is 2xp, which is consistent with the Berry-Keating conjecture. While H is not Hermitian in the conventional sense, while <^> H is PT symmetric with a broken PT symmetry, thus allowing for the possibility that all eigenvalues of H 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 H is manifestly self-adjoint, then this implies that the Riemann hypothesis holds true.
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