Relativistic wavefunctions on the Poincare group
Mathematical Physics
2009-11-10 v2 Group Theory
math.MP
Abstract
The Biedenharn type relativistic wavefunctions are considered on the group manifold of the Poincar\'{e} 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 ten-parameter set of the Poincar\'{e} group. An explicit construction of the wavefunction for the spin 1/2 is given. A relation of the proposed description with the quantum field theory and harmonic analysis on the Poincar\'{e} group is discussed.
Cite
@article{arxiv.math-ph/0308038,
title = {Relativistic wavefunctions on the Poincare group},
author = {V. V. Varlamov},
journal= {arXiv preprint arXiv:math-ph/0308038},
year = {2009}
}
Comments
11 pages