Hamiltonians in Relativistic Classical Particle Mechanics

Abstract

Generators and Lie-bracket relations for the Poincaré group are used to develop a relativistic Hamiltonian formalism, with noncanonical Lorentz transformations, in terms of particle positions and canonical momenta. The usual transformations of particle positions are assumed, and are used to establish the correspondence between the Lie-bracket relations and invariance of the Newtonian equations of motion. The impossibility of interaction for two particles is proved assuming one property of canonical Lorentz transformations: the conventional Lorentz transformations of total energy, momentum, and angular momentum.