A symmetry perspective of the Riemann zeros

• URL: http://arxiv.org/abs/2309.01382v1
• Date: Mon, 4 Sep 2023 06:20:09 GMT
• Title: A symmetry perspective of the Riemann zeros
• Authors: Pushpa Kalauni, Prasanta K. Panigrahi
• Abstract summary: We show that unbroken supersymmetry is associated with the presence of non-trivial zeros of the zeta function. In other cases, supersymmetry is spontaneously broken and the ground state energy of the system is not zero. Our findings provide insights into a $SU(2)$ symmetry that arises within these systems, with the Hilbert space having a two-level structure.
• Score: 0.9790236766474201
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the relationship between the zeros of the Riemann zeta function and physical systems exhibiting supersymmetry, $PT$ symmetry and $SU(2)$ group symmetry. Our findings demonstrate that unbroken supersymmetry is associated with the presence of non-trivial zeros of the zeta function. However, in other cases, supersymmetry is spontaneously broken and the ground state energy of the system is not zero. Moreover, we have established the manifestation of PT symmetry invariance within our supersymmetric system. In addition, our findings provide insights into a $SU(2)$ symmetry that arises within these systems, with the Hilbert space having a two-level structure.

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