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arXiv · 1406.0160

Topological Dirac variables in Abelian $U(1)$ theory

Leonid Lantsman
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Abstract

In this study we, remembering the experience with topological Dirac variables in the non-Abelian Yang-Mills-Higgs (YMH) model with vacuuum BPS monopole solutions, attempt to construct similar for the Abelian $U(1)$ model. We show that QED, as one understands it commonly, is only the topologically trivial sector ($n=0$) of this Abelian $U(1)$ model. For $n\neq 0$ one gets Dirac monopole modes. In both the cases, $n=0$ and $n\neq 0$, the theory can be quantized via the Hamiltonian reduction in terms of Dirac variables.

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Leonid Lantsman. 2014-06-01. Topological Dirac variables in Abelian $U(1)$ theory. https://arxiv.org/abs/1406.0160

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