Construction of Invariant Scalar Amplitudes
without Kinematical Singularities for
Arbitrary-Spin Nonzero-Mass
Two-Body Scattering Processes

David N. Williams

September 9, 1967

Lawrence Radiation Laboratory
University of California, Berkeley

Abstract: The relativistic transition amplitude for any two-body reaction involving only particles of nonzero mass but arbitrary spin is decomposed in terms of scalar amplitudes that are regular functions in the space of scalar invariants at points corresponding to regular points of the transition matrix elements in momentum space, on the mass shell. Detailed formulas for the scalar amplitudes in terms of the original scattering matrix elements are given. The development is in the framework of analytic S-matrix theory, and is based on a partial generalization of the Hall-Wightman Theorem. The results hold on the complete (multisheeted) domain of regularity of the scattering amplitude.

Back to webprints
Back to home page.