Eur. Phys. J. C 22, 581-584 (2001)
DOI: 10.1007/s100520100832

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

R.A. Frick

Institut für Theoretische Physik, Universität Köln, 50923 Köln, Germany

(Received: 20 September 2001 / Published online: 23 November 2001 - © Springer-Verlag / Società Italiana di Fisica 2001 )

Abstract
In a generalized Heisenberg/Schrödinger 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.

© Società Italiana di Fisica, Springer-Verlag 2001