An Analytic Continuation of Propagators in a Particle-Exchange Model

概要

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From the viewpoint that information on the behaviour of a desirable propagator at p_μ=0 is provided in the analysis of kinematical singularities at p_μ=0, we examine an analytic continuation of the conventional propagator under the assumption that the tracelessness property together with the symmetry property survives even in the presence of interactions. By using the propagator thus obtained, we can construct the Lorentz poles in the Van Hove model. We obtain full amplitude as a closed form summed over all the partial waves. This follows from the decomposition of the propagator to lower spin states by using orthogonal projection operators. The unitarized propagator has the correct O (4) structure at the symmetry point when certain restrictions are imposed on the self-energy parts and yields families of J-plane poles which move with energy. Calculations on the self-energy parts in a model-dependent manner suggest that it is unlikely that daughter trajectories are parallel to the parent trajectory.
理論物理学刊行会の論文
1974-07-25