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

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 $n\ne 0$ one gets Dirac monopole modes. In both the cases, $n=0$ and $n\ne 0$, the theory can be quantized via the Hamiltonian reduction in terms of Dirac variables.

The Coulomb law for two magnetic charges is recorded manifestly on p. 48. arXiv admin note: text overlap with arXiv:hep-th/0109218 by other authors

References in corpus (8)

• Monopole Vacuum in Non-Abelian Theories
• Dirac fundamental quantization of gauge theories is natural way of reference frames in modern physics
• The Higgs field as the Cheshire cat and his Yang-Mills "smiles"
• Minkowskian Yang-Mills vacuum
• Superfluidity of Minkowskian Higgs vacuum with BPS monopoles quantized by Dirac may be described as Cauchy problem to Gribov ambiguity equation
• "Discrete" vacuum geometry as a tool for Dirac fundamental quantization of Minkowskian Higgs model
• Nontrivial topological dynamics in Minkowskian Higgs model quantized by Dirac
• Interpreting Dirac variables in terms of the Hilbert space of gauge-invariant and Poincare-covariant states