Unitary representation of the Poincar\'e group for classical relativistic dynamics

Abstract

We give a unitary irreducible representation of the proper Poincar\'e group that leads to an operational version of the classical relativistic dynamics of a massive spinless particle. Unlike quantum mechanics, in this operational theory there is no uncertainty principle between position and momentum. It will be shown that the theory contains the Koopman-von Neumann formalism as a particular case, and a explicit connection with relativistic Hamiltonian mechanics will be given.