Composite Particle and Vertex Function in the Nonrelativistic Off-Shell Theory

概要

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We extend Weinberg's quasiparticle method to the useful form having good correspondence to the on-shell S-matrix theory and giving a unique definition of vertex function and propagator of composite particle in the nonrelativistic off-shell theory. A method is proposed, by which the off-shell scattering amplitude is separated into two parts: one having no composite particle pole and satisfying the unitarity under the on-shell condition, and the other consisting of vertex functions and propagator related to the composite particle. This new separation has complete correspondence to the one in the usual on-shell S-matrix theory. It is shown that proper and improper vertex functions and form factor, which satisfy the on-shell unitarity, can be defined in the off-shell theory by using Weinberg's eigenfunction. Analytic continuation formulas for the form factor, vertex functions and amplitudes into the second sheet are obtained in rather peculiar forms. Further, it is shown that both bound state and resnance can be treated in the parallel way.
理論物理学刊行会の論文
1967-05-25