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Dirac's Quantization of Maxwell's Theory on Non-Commutative Spaces

S. I. Kruglov
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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.

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S. I. Kruglov. 2002-06-03. Dirac's Quantization of Maxwell's Theory on Non-Commutative Spaces. https://arxiv.org/abs/quant-ph/0204137

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