Supersymmetric quantum mechanics and the Riemann hypothesis

Abstract

We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally correspond to the vanishing ground state energies in this model. The model provides a natural form of supersymmetry.

arXiv comment5 pages, 1 figure

References in corpus (13)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Physics of the Riemann Hypothesis
• Hamiltonian for the zeros of the Riemann zeta function
• Will a physicist prove the Riemann Hypothesis?
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Should PT symmetric quantum mechanics be interpreted as nonlinear?
• An alternative construction of the positive inner product in non-Hermitian quantum mechanics
• An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples
• The B-mode polarization of CMB and Cosmic Neutrino Background
• Supersymmetry and the Riemann zeros on the critical line
• Asymptotic analysis on a pseudo-Hermitian Riemann-zeta Hamiltonian
• Operator-valued zeta functions and Fourier analysis

Cited by in corpus (1)

• A symmetry perspective of the Riemann zeros