Relativistic Particle Dynamics and the S Matrix

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Abstract
Direct‐interaction theories are examined from the viewpoint of relativistic scattering theory and the associated concept of ``asymptotic covariance.'' It is pointed out that with any two‐particle Hamiltonian which has no bound states there can be associated a variety of representations of the Lie algebra of the inhomogeneous Lorentz group (IHLG), although the S matrix is in general not covariant. 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 the 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 is made. The 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. It is also proved that relativistic Hamiltonians of this type do not admit the usual notion of a coupling constant.

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