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arXiv · 1304.5342

Modular forms in Quantum Field Theory

Francis Brown·Oliver Schnetz
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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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Francis Brown, Oliver Schnetz. 2013-04-19. Modular forms in Quantum Field Theory. https://arxiv.org/abs/1304.5342

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