Symplectic Dirac Equation
Mathematical Physics
2016-03-30 v1 High Energy Physics - Theory
math.MP
Abstract
Symplectic unitary representations for the Poincar\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.
Cite
@article{arxiv.1504.03041,
title = {Symplectic Dirac Equation},
author = {R. G. G. Amorim and S. C. Ulhoa and Edilberto O. Silva},
journal= {arXiv preprint arXiv:1504.03041},
year = {2016}
}