Amplitudes and the Riemann Zeta Function

2021/08/17 by Grant N. Remmen · 1 voice
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP

paper · pdf · doi:10.1103/physrevlett.127.241602

published as Phys. Rev. Lett 127, 241602 (2021), Editors' Suggestion · 5 pages, 2 figures

arxiv published 2021/08/17 · arxiv created 2021/12/08 · arxiv updated 2021/12/09

Abstract

Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses m_n² = μ_n², where ζ((1)/(2) ± iμ_n) = 0. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of ζ. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of 1/μ_n².

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Discussions

• Highly technical, but I can't resist pointing to this new paper by Grant Remmen. It connects the Riemann zeta function to scattering amplitudes in a certain quantum field theory. Particle masses would [bsky, 0 points, 1 comments]

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