Cubic root of KleinGordon equation
Abstract
We construct new relativistic linear differential equation in d dimensions generalizing Dirac equation by employing the Clifford algebra of the cubic polynomial associated to KleinGordon 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 anyonlike fields in /d=1+1. Coupling to a U(1) gauge field is discussed and compared with Dirac theory.
 Publication:

Physics Letters B
 Pub Date:
 March 2000
 DOI:
 10.1016/S03702693(00)001908
 arXiv:
 arXiv:hepth/0001067
 Bibcode:
 2000PhLB..477..276P
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 12 pages, typos corrected. To appear in Phys. Lett. B