Minkowskian Yang-Mills vacuum

Abstract

The well-known Bogomol'nyi-Prasad-Sommerfeld (BPS) monopole is considered in the limit of the infinite mass of the Higgs field as a basis for constructing the Yang-Mills vacuum with the finite energy density. In this limit the Higgs field disappears at the spatial infinity, but it leaves, nevertheless, its trace as vacuum Yang-Mills BPS monopoles transformed into Wu-Yang monopoles obtained in the pure Yang-Mills theory by a spontaneous scale symmetry breaking in the class of functions with zero topological charges. The topological degeneration of a vacuum BPS monopole manifests itself via Gribov copies of the covariant Coulomb gauge in the form of the time integral of the Gauss law constraint. We also show that, in the considered theory, there is a zero mode of the Gauss constraint involving an "electric" monopole and the additional mass of the ${\eta }^{\prime }$-meson in Minkowskian QCD. The consequences of the Minkowskian physical monopole vacuum: rising "golden section" potential and topological confinement, are studied in the framework of the perturbation theory. An estimation of the vacuum expectation value of the square of the magnetic tension is given through the ${\eta }^{\prime }$-meson mass, and arguments in favour of the stability of the monopole vacuum are considered. We also discuss why all these "smiles" of the Cheshire cat are kept by the Dirac fundamental quantization, but not by the conventional Faddeev-Popov integral.

LaTeX file, 56 pages, the TEX corrections

References in corpus (5)

• Monopole Vacuum in Non-Abelian Theories
• Dirac variables in gauge theories
• Gribov ambiguities and the fundamental domain
• Topological invariant variables in QCD
• Nonperturbative and analytical approach to Yang-Mills thermodynamics

Cited by in corpus (7)

• Superfluid properties of BPS monopoles
• "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
• BPS ansatzes as electric form-factors
• Whether the vacuum manifold in the Minkowskian non-Abelian model quantized by Dirac can be described with the aid of the superselection rules?
• Topological Dirac variables in Abelian $U(1)$ theory