Infinite Products and Convergence Properties of Certain Reggeized Feynman Diagrams

Certain of the Reggeized Feynman diagrams suggested by Kikkawa, Klein, Sakita, and Virasoro that require integrals of infinite products of functions are examined. Methods are formulated for explicitly evaluating the infinite products that occur in simple examples of the class of one-loop nonplanar Reggeized Feynman diagrams whose duals are homeomorphic to a sphere with two windows. The infinite products are found to cause the integrals in these cases to diverge, necessitating a regularizing procedure. The integrals can be given meaning by a redefinition which produces an unwanted pole in the square of the sum of the momenta associated with either window, or with a certain type of smoothing function.