Interpreting Dirac variables in terms of the Hilbert space of gauge-invariant and Poincare-covariant states

Abstract

The goal of this note is to give a description of Dirac variables in Abelian as well as non-Abelian gauge models in terms of gauge-invariant and Poincare-covariant states sweeping a Hilbert space ${\mathcal{H}}_{\mathrm{vac}}$. The next our conjecture concerns the spontaneous breakdown of the Abelian U(1) symmetry in the 'discrete' $U(1)\to \mathbf{Z}$ wise. We suppose that gauge charges are preserved in this case.

17 pages, the wrong conclusion about Dirac variables is deleted

References in corpus (6)

• 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

Cited by in corpus (1)

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