Publication : t13/218

The physics and the mixed Hodge structure of Feynman integrals

Vanhove P. (CEA, IPhT (Institut de Physique Théorique), F-91191 Gif-sur-Yvette, France)
This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining that the first Symanzik polynomial is the determinant of the period matrix of the graph, and the second Symanzik polynomial is expressed in terms of world-line Green's functions. We then review the relation between Feynman graphs and variations of mixed Hodge structures. Finally, we provide an algorithm for generating the Picard-Fuchs equation satisfied by the all equal mass banana graphs in a two-dimensional space-time to all loop orders.
Année de publication : 2013
DOI : 10.1090/pspum/088/01455
Preprint : arXiv:1401.6438
Langue : Anglais


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