Dirac's Quantization of Maxwell's Theory on Non-Commutative Spaces
Abstract
Dirac's quantization of the Maxwell theory on non-commutative spaces has been considered. First class constraints were found which are the same as in classical electrodynamics. The gauge covariant quantization of the non-linear equations of electromagnetic fields on non-commutative spaces were studied. We have found the extended Hamiltonian which leads to equations of motion in the most general gauge covariant form. As a special case, the gauge fixing approach on the basis of Dirac's brackets has been investigated. The problem of the construction of the wave function and physical observables have been discussed.
Cite
@article{arxiv.quant-ph/0204137,
title = {Dirac's Quantization of Maxwell's Theory on Non-Commutative Spaces},
author = {S. I. Kruglov},
journal= {arXiv preprint arXiv:quant-ph/0204137},
year = {2007}
}
Comments
14 pages, LaTex, added a discussion of phenomenological consequences of NCQED and references. Prepared for special issue of "Electromagnetic Phenomena", dedicated to Dirac