1304.5342 (Francis Brown et al.)

Modular forms in Quantum Field Theory    [PDF]

Francis Brown, Oliver Schnetz

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, of 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.

View original: http://arxiv.org/abs/1304.5342