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Modular forms in Quantum Field Theory

Algebraic Geometry 2013-06-28 v2 High Energy Physics - Theory

Abstract

The amplitude of a Feynman graph in Quantum Field Theory is related to the point-count over finite fields of the corresponding graph hypersurface. This article reports on an experimental study of point counts over F_q modulo q^3, for graphs up to loop order 10. It is found that many of them are given by Fourier coefficients of modular forms of weights <=8 and levels <=17.

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Cite

@article{arxiv.1304.5342,
  title  = {Modular forms in Quantum Field Theory},
  author = {Francis Brown and Oliver Schnetz},
  journal= {arXiv preprint arXiv:1304.5342},
  year   = {2013}
}

Comments

27 pages

R2 v1 2026-06-22T00:02:48.753Z