Construction of Invariant Scattering Amplitudes for Arbitrary Spins and Analytic Continuation in Total Angular Momentum

From group-theoretical considerations, invariant scattering amplitudes for two-body reactions of particles with arbitrary spins and nonzero masses are constructed in various forms, including helicity amplitudes and amplitudes free of kinematical singularities. They are linear combinations of spin basis functions with scalar coefficients. In the process of construction the Pauli spin matrices are generalized for arbitrary spin. On the basis of a Mandelstam representation for the scalar coefficients, the unique analytic continuation of the amplitudes in total angular momentum is obtained. Possible kinematical singularities of the scalar amplitudes at the boundary of the physical region are discussed.