The representations of the Poincaré group as functions of the eigenvalues of casimir operators

In this paper explicit basis functions are defined for the Poincaré group. Both these functions and the representation matrix elements are continuous functions of the momentum variables for the whole real p² spectrum, including the p² = 0 point. The essence of our method is to enlarge previously obtained SL(2, C) basis functions and representations of a similar nature.