Classical particle systems. I. Galilei free particle

Abstract

This is the first of a series of papers concerning the group theoretical approach to the classical particle systems, related to a definite special relativity principle and which are explicitly expressed in a Lagrangian formalism. In the Galilei case, the free classical particle can be characterised by its mass, internal energy and spin, similarly in the quantal version. The spin appears as a derived observable related to the orientation and to the internal motion of the system and has in general three parts; one of intrinsic nature, one, like a spherically symmetric body, related to the angular velocity and a third which is the (anti)orbital part of the relative motion of the system around its centre of mass. Galilei photons are massless particles, with spin and linear momentum lying along the direction of motion, travelling at infinite speed and carrying no energy. The Lagrangian of a free particle with intrinsic spin is no longer time-reversal invariant.