Non-Abelian observable-geometric phases and the Riemann zeros

• URL: http://arxiv.org/abs/2403.19118v1
• Date: Thu, 28 Mar 2024 03:23:46 GMT
• Title: Non-Abelian observable-geometric phases and the Riemann zeros
• Authors: Zeqian Chen,
• Abstract summary: We introduce the notion of non-Abelian observable-geometric phases. Since the observable-geometric phases are connected with the geometry of the observable space, this sheds some light on the investigation of the Heisenberg equation.
• Score: 1.3597551064547502
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The Hilbert-P\'{o}lya conjecture asserts that the imaginary parts of the nontrivial zeros of the Riemann zeta function (the Riemann zeros) are the eigenvalues of a self-adjoint operator (a quantum mechanical Hamiltonian, in the physical sense), as a promising approach to prove the Riemann hypothesis (cf.\cite{SH2011}). Instead of the eigenvalues, in this paper we consider observable-geometric phases as the realization of the Riemann zeros in a periodically driven quantum system, which were introduced in \cite{Chen2020} for the study of geometric quantum computation. To this end, we further introduce the notion of non-Abelian observable-geometric phases, involving which we give an approach to finding a physical system to study the Riemann zeros. Since the observable-geometric phases are connected with the geometry of the observable space according to the evolution of the Heisenberg equation, this sheds some light on the investigation of the Riemann hypothesis.

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