Schouten identities for Feynman graph amplitudes; The Master Integrals for the two-loop massive sunrise graph

A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two-loop sunrise graph with arbitrary masses for recovering the second-order differential equation for the scalar amplitude in d = 2 dimensions, as well as a chained set of equations for all the coefficients of the expansions in (d - 2). The shift from d approximate to 2 to d approximate to 4 dimensions is then discussed. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP(3).