We construct new relativistic linear differential equation in $d$ dimensions
generalizing Dirac equation by employing the Clifford algebra of the cubic
polynomial associated to Klein-Gordon operator multiplied by the mass
parameter. Unlike the Dirac case where the spin content is unique and Lorentz
covariance is manifest, here the spin as well as Lorentz covariance of the
theory are related to the choice of representation of the Clifford algebra. One
of the considered explicit matrix representations gives rise to anyon-like
fields in $d=1+1$. Coupling to a U(1) gauge field is discussed and compared
with Dirac theory.
Publié le : 2000-01-11
Classification:
High Energy Physics - Theory,
General Relativity and Quantum Cosmology,
High Energy Physics - Phenomenology,
Mathematical Physics,
Quantum Physics
@article{0001067,
author = {Plyushchay, Mikhail S. and de Traubenberg, Michel Rausch},
title = {Cubic root of Klein-Gordon equation},
journal = {arXiv},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/0001067}
}
Plyushchay, Mikhail S.; de Traubenberg, Michel Rausch. Cubic root of Klein-Gordon equation. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0001067/