Behaviour of Masses and Coupling Constants in Two Processes Involving Vanishing Z_3

概要

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The processes of taking the limit of vanishing Z_3 are investigated without any restriction on the number of particle states and free parameters in a single channel. These limiting processes are classified into two kinds, according to whether the scattering amplitude goes into its one-particle irreducible part or not. The former process is understood to be the decoupling limit of the interaction of a bare field which appears in the one-particle intermediate state, and the latter to be the direct interaction limit of the propagation of the bare field. For the many-pole amplitude with a finite bare mass, a one-to-one correspondence is obtained between the physical particle poles and the set consisting of pseudo-particle poles plus a bare particle. In the former process involving vanishing Z_3, a physical particle pole tends to the bare field with the interaction switched off and the other physical particle poles tend to corresponding pseudo-particle poles. In the latter process, the bare mass tends to infinity and the information about the bare field remains in the form of a direct interaction. Any amplitude can be regarded as obtained from another one by these limiting processes. This fact implies an ambiguity in separating an amplitude into the modified Born term and the one-particle irreducible part.
理論物理学刊行会の論文
1966-08-25