Power counting and regularization through loop integrations for multiple Feynman integrals in Minkowski space

A regularization procedure with a regularization parameter is developed which may be applied to multiple Feynman integrals in Minkowski space. The regularization is carried out inmomentum space and provides a rigorous method for studying Feynman integrals as multiple integrals in real variable theory. The regularized integrals are defined by changing the measure of integration _idx_i to _i(1+x_i²)^–/2dx_i, >0, with a corresponding change defined inMinkowski space. We then develop a power counting convergence criterion for the absolute convergence of the integrals in terms of the parameter as a function of the so-called power asymptotic coefficients of Feynman integrands. An application to quantum electrodynamics is carried out.Work supported by the Department of National Defence Award under CRAD No. 3610-637:F4122.