RELATIVISTIC DIRECT INTERACTION THEORIES.
MARYLAND UNIV COLLEGE PARK
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Direct interaction theories are examined for the viewpoint of relativistic scattering theory and the associated concept of asymptotic covariance. It is pointed out that with any twoparticle Hamiltonian which has no bound states there can be associated a variety of representations of the Lie algebra of the inhomogeneous Lorentz group IHLG. It is shown that the requirement of asymptotic covariance ensures both the covariance of the S-matrix and the existence of a unique representation of the IHLG to be associated with a relativistic two-particle system. The connection between the Lie algebra, the covariant form of the S-matrix, and the uniqueness of K, the generator of pure Lorentz transformations, is thereby clarified. The extension of these considerations to include bound states and production processes is made. The two-particle form of H given by Bakamjian and Thomas is shown to satisfy asymptotic covariance and, moreover, to be the most general form of interest from the viewpoint of relativistic scattering theory, thereby including as a special case a form of H suggested by Sudarshan. Author