Geodesic
Feynman amplitudes and limits of heights
Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 813-848

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We investigate from a mathematical perspective how Feynman amplitudes appear in the low-energy limit of string amplitudes. In this paper, we prove the convergence of the integrands. We derive this from results describing the asymptotic behaviour of the height pairing between degree-zero divisors, as a family of curves degenerates. These are obtained by means of the nilpotent orbit theorem in Hodge theory.
Keywords: low-energy limit, asymptotics of the archimedean height pairing, Symanzik polynomials, nilpotent orbit theorem, biextension mixed Hodge structures, regularized Green functions.
Mots-clés : Feynman amplitudes 
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     title = {Feynman amplitudes and limits of heights},
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O. Amini; S. J. Bloch; J. I. Burgos Gil; J. Fresán. Feynman amplitudes and limits of heights. Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 813-848. http://geodesic.mathdoc.fr/item/IM2_2016_80_5_a1/