Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups
| Autor: | Magazev, Alexey A. |
|---|---|
| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Theoretical and Mathematical Physics, December 2012, Volume 173, Issue 3, pp 1654-1667 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s11232-012-0139-x |
| Popis: | We investigate the structure of the Klein-Gordon-Fock equation symmetry algebra on pseudo-Riemannian manifolds with motions in the presence of an external electromagnetic field. We show that in the case of an invariant electromagnetic field tensor, this algebra is a one-dimensional central extension of the Lie algebra of the group of motions. Based on the coadjoint orbit method and harmonic analysis on Lie groups, we propose a method for integrating the Klein-Gordon-Fock equation in an external field on manifolds with simply transitive group actions. We consider a nontrivial example on the four-dimensional group $E(2) \times \mathbb{R}$ in detail. Comment: 16 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|