Representations of the Poincare group on relativistic phase space
Abstract
We introduce a complex relativistic phase space as the space 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 Poincar\'{e} 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.
Keywords
Cite
@article{arxiv.0802.0070,
title = {Representations of the Poincare group on relativistic phase space},
author = {Yaakov Friedman},
journal= {arXiv preprint arXiv:0802.0070},
year = {2008}
}