Relativistic Mechanics of Interacting Particles and Multi-Local Theory. I: The Bilocal Case

Abstract

Relativistic mechanics of two-particle system, where the two constituent particles are bound by an arbitrary scalar potential, is derived from a Lagrangian completely. This Lagrangian has a new kind of invariance which gives rise to a primary constraint responsible to the suppression of the relative time degree. The other primary constraint following from the Lagrangian determines the rest mass of the system as due to internal motion. These constraints, together with the Euler equations, define the relativistic mechanics of the system in such a way that it has clear physical interpretation. Equivalence of this theory with the relativistic mechanics of two interacting particles established in a previous paper is explicitly shown. Quantization and introduction of interactions are briefly explained.