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

TL;DR

This paper develops a unitary irreducible representation of the Poincaré group to formulate a classical relativistic dynamics framework for a massive spinless particle, connecting it with Hamiltonian mechanics and the Koopman-von Neumann formalism.

Contribution

It introduces a novel operational classical relativistic dynamics model based on Poincaré group representations, distinct from quantum mechanics.

Findings

Provides a unitary irreducible representation of the Poincaré group for classical dynamics.

Shows the theory contains the Koopman-von Neumann formalism as a special case.

Establishes a connection with relativistic Hamiltonian mechanics.

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.