Relativistic wavefunctions on the Poincaré group
Abstract
The Biedenharn type relativistic wavefunctions are considered on the group manifold of the Poincaré group. It is shown that the wavefunctions can be factorized on the group manifold into translation group and Lorentz group parts. A Lagrangian formalism and field equations for such factorizations are given. Parametrizations of the functions obtained are studied in terms of a tenparameter set of the Poincaré group. An explicit construction of the wavefunction for spin 1/2 is given. A relation of the proposed description with quantum field theory and harmonic analysis on the Poincaré group is discussed.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 May 2004
 DOI:
 10.1088/03054470/37/20/014
 arXiv:
 arXiv:mathph/0308038
 Bibcode:
 2004JPhA...37.5467V
 Keywords:

 Mathematical Physics;
 Mathematics  Group Theory;
 22E43;
 35Q40;
 22E70
 EPrint:
 11 pages