Relativistic Mechanics of Interacting Particles and Multi-Local Theory. II: Trilocal and More General Cases

概要

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New classical theory of relativistic composite system consisting of three point particles is set up, where particles are bound by arbitrary spacelike action-at-a-distance. The theory is derived completely from a Lagrangian, which has certain invariance properties giving rise to primary constraints that ensure clear physical interpretation of theory. The case where the force potential is of Hooke-type is explicitly solved and various modes of motions are classified. Quantization leads to a trilocal wave equation associated with subsidiary conditions. This is regarded as representing a prototype of relativistic quark model of baryonic states. It is also shown that an alternative Lagrangian with higher invariance gives a trilocal model which admits 'relativistic restricted rigid motions' alone. Extension of the present method is discussed to show that relativistic composite systems have priviledged simplicity when they consist of two, three and four particles in the sense that the present simple scheme is applicable to those cases alone.
理論物理学刊行会の論文
1977-10-25