Propagator and Vertex Function of a Bound State in the Green's Function Formalism

概要

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On the basis of the scattering Green's function formalism, definitions of the propagator and the vertex function corresponding to a bound state are proposed in such a way that they coincide with the conventional definitions if the state considered happens to be an elementary particle. They are required to satisfy certain integral equations and three additional requirements. The appropriateness of these conditions is discussed in a chain model and in a modified chain model. The Zachariasen model is also discussed in connection with the renormalization problem. It is demonstrated how to find the propagators and the vertex functions of bound states in the Wick-Cutkosky model and in the ladder model for non-zero exchanged-meson mass, and they are explicitly found in some special cases of the former model. The definition of the bound-state field operator due to Nishijima, Zimmermann and Haag is discussed in the Green's function formalism and compared with the above definition of the bound-state propagator.
理論物理学刊行会の論文
1966-10-25