Complex Angular Momenta and Many-Particle States. I. Properties of Local Representations of the Rotation Group

The properties of the ``local representations'' of the rotation group corresponding to complex angular momentum are further developed. Completeness and bi-orthogonality relations are derived and a reduction of products is carried out, giving a generalization of the Clebsch-Gordan reduction. The connection with the representation theory of the group SL(2,R) is considered and a generalization of Regge's use of the Sommerfeld-Watson transform is made to the case where three momentum transfer variables occur in the description of scattering amplitudes.