Integral representation for the dimensionally regularized massive Feynman amplitude

Abstract

A convergent integral representation for the massive Feynman amplitude in complex dimension D is defined away from ReD equal to some rationals. The Feynman integrand is modified according to the technique of Zimmermann’s forests but each subgraph is subtracted at zero external momenta and zero internal masses; the order of the Taylor subtractions depends upon ReD. The so defined regularized Feynman amplitude is a meromorphic function of D with multiple poles at some rationals, which satisfies field equations and Ward identities. These amplitudes may be used in the construction of a bare Lagrangian field theory.