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Register a new userAnalysis of constraints in light-cone version of SU(2) Yang-Mills mechanics
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We study the classical dynamics of mechanical model obtained from the light-cone version of SU(2) Yang-Mills field theory under the supposition of gauge potential dependence only on ``time along the light-cone direction. The computer algebra system Maple was used strongly to compute and separate the complete set of constraints. In contrast to the instant form of Yang-Mills mechanics the constraints here represent a mixed form of first and second-class constraints and reduce the number of the physical degrees of freedom up to four canonical one.
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We examine the mechanical matrix model that can be derived from the SU(2) Yang-Mills light-cone field theory by restricting the gauge fields to depend on the light-cone time alone. We use Diracs generalized Hamiltonian approach. In contrast to its well-known instant-time counterpart the light-cone version of SU(2) Yang-Mills mechanics has in addition to the constraints, generating the SU(2) gauge transformations, the new first and second class constraints also. On account of all of these constraints a complete reduction in number of the degrees of freedom is performed. It is argued that the classical evolution of the unconstrained degrees of freedom is equivalent to a free one-dimensional particle dynamics. Considering the complex solutions to the second class constraints we show at this time that the unconstrained Hamiltonian system represents the well-known model of conformal mechanics with a ``strength of the inverse square interaction determined by the value of the gauge field spin.
We consider spatial coarse-graining in statistical ensembles of non-selfintersecting and one-fold selfintersecting center-vortex loops as they emerge in the confining phase of SU(2) Yang-Mills thermodynamics. This coarse-graining is due to a noisy environment and described by a curve shrinking flow of center-vortex loops locally embedded in a two-dimensional flat plane. The renormalization-group flow of an effective `action, which is defined in purely geometric terms, is driven by the curve shrinking evolution. In the case of non-selfintersecting center-vortex loops, we observe critical behavior of the effective `action as soon as the center-vortex loops vanish from the spectrum of the confining phase due to curve shrinking. This suggest the existence of an asymptotic mass gap. An entirely unexpected behavior in the ensemble of one-fold selfintersecting center-vortex loops is connected with the spontaneous emergence of order. We speculate that the physics of planar, one-fold selfintersecting center-vortex loops to be relevant for two-dimensional systems exhibiting high-temperature superconductivity.
We develop numerical tools and apply them to solve the relativistic Yang--Mills--Higgs equations in a model where the SU(N) symmetry is spontaneously broken to its center. In SU(2) and SU(3), we obtain the different field profiles for infinite and finite center vortices, with endpoints at external monopole sources. Exploration of parameter space permits the detection of a region where the equations get Abelianized. Finally, a general parametrization of the color structure of SU(2) fields leads us to a reference point where an Abelian-like BPS bound is reconciled with N-ality.
As shown by Taubes, in the Bogomolnyi-Prasad-Sommerfield limit the SU(2) Yang-Mills-Higgs model possesses smooth finite energy solutions, which do not satisfy the first order Bogomolnyi equations. We construct numerically such a non-Bogomolnyi solution, corresponding to a monopole-antimonopole pair, and extend the construction to finite Higgs potential.
By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links bounded by the closed 2-dimensional center vortex surfaces. The center field propagator is found to dominate the gluon propagator (in Landau gauge) in the low momentum regime and to give rise to an OPE correction to the latter of ${sqrt{sigma}}/{p^3}$.The screening mass of the center vortex field vanishes above the critical temperature of the deconfinement phase transition, which naturally explains the second order nature of this transition consistent with the vortex picture. Finally, the ghost propagator of maximal center gauge is found to be infrared finite and thus shows that the coset fields play no role for confinement.
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