The Discontinuity of a General Feynman Integral and Regge Poles in Perturbation Theory.

摘要

A formula for the complete discontinuity across the cut of an arbitrary Feynman integral is derived. One-variable dispersion relations for a certain range of the other variable are established. Mellin transforms are extended to Feynman integrals with indefinite coefficients of s and t in the Feynman denominator. This extension is non-trivial. Finally a method is derived that allows treatment of the leading asymptotic behaviour in terms of Legendre functions instead of only in terms of powers of the variable going to infinity. It is shown that in all cases in which a leading (-t) exp.((alpha sub i) (s)) behaviour has been obtained for a class of Feynman integrals summed, a Regge pole can explicitely be shown to exist in the Regge plane. The pole structure in the Regge plane is shown to be simpler than the one in the alpha plane. (Author)