Propagation of a relativistic particle in terms of the unitary irreducible representations of the Lorentz group

TL;DR

This paper presents a framework for describing the propagation of relativistic particles using unitary irreducible representations of the Lorentz group, linking invariant space-time transformations with relativistic mechanics.

Contribution

It introduces a novel approach to particle propagation based on Lorentz group representations and invariant transformations, including the use of light-cone vectors and Casimir operators.

Findings

Particle propagation defined as space-time transition between states with equal Casimir eigenvalues

Framework applicable to massive spin-0 particles and their nonrelativistic limit

Establishes connection between relativistic mechanics and group-theoretic representations

Abstract

In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the particle may be defined as space-time transition between states with equal eigenvalues of the first and second Casimir operators of the Lorentz algebra. In addition we use a vector on the light-cone. A massive relativistic particle with spin 0 is considered. We also consider the nonrelativistic limit.