2006/06/06 by Martin Land, Land, Martin
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0606046
25 pages
arxiv created 2006/06/06 · arxiv updated 2009/12/01
In a previous paper, we found an extension of the N-dimensional Lorentz generators that partially restores the closed operator algebra in the presence of a Maxwell field, and is conserved under system evolution. Generalizing the construction found by Berard, Grandati, Lages and Mohrbach for the angular momentum operators in the O(3)-invariant nonrelativistic case, we showed that the construction can be maximally satisfied in a three dimensional subspace of the full Minkowski space; this subspace can be chosen to describe either the O(3)-invariant space sector, or an O(2,1)-invariant restriction of spacetime. When the O(3)-invariant subspace is selected, the field solution reduces to the Dirac monopole field found in the nonrelativistic case. For the O(2,1)-invariant subspace, the Maxwell field can be associated with a Coulomb-like potential on spacetime, similar to that used by Horwitz and Arshansky to obtain a covariant generalization of the hydrogen-like bound state. In this paper we elaborate on the generalization of the Dirac monopole to N-dimensions.