Decomposition Of Non-Abelian Gauge Potential, Qcd Vacuum Structure And Relevant Issues

In this thesis, based on the decomposition of gauge potential, we mainly discusse the QCD vacuum, knot configurations in CP1model and generalized Skyrme-Faddeev model. Then we propose a new type of monopole configuration without local monopole charge in QCD. The non-Abrikosov vortices in the two-component superconductor are investigated in the last part.We consider topological structure of the classical vacuum in quantum QCD. In the framework of formalism of gauge invariant Abelian projection, we show that classical vacuums can be constructed in terms of Killing vector fields on the group SU(3). Consequently, homotopic classes of Killing vector fields de-termine the topological structure of the vacuum. Starting with a given Killing vector field, one can construct vacuums forming a Weyl sextet representation. An interesting feature of SU(3) gauge theory is that it admits a Weyl symmetric vacuum represented by a linear superposition of the vacuums from the Weyl vac-uum sextet. A nontrivial manifestation of the Weyl symmetry is demonstrated on monopole solutions. We construct a family of finite energy monopole solutions in Yang-Mills-Higgs theory that includes the Weyl monopole sextet.In part Ⅱ, we study the knot topology of QCD classical vacuum. Starting with explicit vacuum knot configurations we study possible exact classical solu-tions as vacuum excitations. Exact analytic non-static knot solution in a simple CP1model in Euclidean space-time has been obtained. We construct an ansatz based on knot and monopole topological vacuum structure for searching new so-lutions in SU(2) and SU(3) QCD. We show that singular knot-like solutions in QCD in Minkowski space-time can be naturally obtained from knot solitons in integrable CP1models. A family of Skyrme type low energy effective theories of QCD admitting exact analytic solutions with non-vanishing Hopf charge is pro-posed. There is a class of knot configuration with Hopf charge QH=m2which energies are proportional to QH1/2, while the normal energy bound for a knot is E≥E0QH3/4.In part III, with the Hopf mapping in knot configuration we propose a new type of regular monopole-like field configuration in QCD and CP1model. The monopole configuration can be treated as a monopole-antimonopole pair without localized magnetic charges. An exact numeric solution for a simple monopole-antimonopole solution has been obtained in CP1model with an appropriate potential term.In the last part, we consider non-Abrikosov vortex solutions in liquid metallic hydrogen (LMH) in the framework of two-component Ginzburg-Landau model, which is an important application of Cho-Duan decomposition in non-Abelian su-perconductor theory. We have shown that there are three types of non-Abrikosov vortices depending on chosen boundary conditions at the core of vortices, namely, Neumann (N)-type, Dirichlet(D)-type and Gross-Pitaevskii (GP)-type vortices. The Neumann-type vortex has a non-vanishing condensation at the core, that is different from the ordinary vortex, and the magnetic flux could be reversed as well in LMH. Furthermore, we have obtained a new type of a neutral vortex which has no magnetic field. The presence of such a vortex is related to metallic superfluid state suggested by Babaev.