Representations of the Poincare group on relativistic phase space
| dc.creator | Friedman, Yaakov | |
| dc.date | 2008-02-01 | |
| dc.date.accessioned | 2026-07-07T09:18:13Z | |
| dc.date.available | 2026-07-07T09:18:13Z | |
| dc.description | We introduce a complex relativistic phase space as the space $\mathbb{C}^4$ equipped with the Minkowski metric and with a geometric tri-product on it. The geometric tri-product is similar to the triple product of the bounded symmetric domain of type IV in Cartan's classification, called the spin domain. We define a spin 1 representations of the Lie algebra of the Poincaré group by natural operators of this tri-product on the complex relativistic phase space. This representation is connected with the electromagnetic tensor. A spin 1/2 representation on the complex relativistic phase space is constructed be use of the complex Faraday electromagnetic tensor. We show that the Newman-Penrose basis for the phase space determines the Dirac bi-spinors under this representation. Quite remarkable that the tri-product representation admits only spin 1 and spin 1/2 representations which correspond to most particles of nature. | |
| dc.identifier | https://arxiv.org/abs/0802.0070 | |
| dc.identifier | http://arxiv.org/abs/0802.0070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/153948 | |
| dc.subject | Mathematical Physics | |
| dc.title | Representations of the Poincare group on relativistic phase space | |
| dc.type | text |