Studies On Nonperturbative Method And Permutation Group Method In Gauge Field Theory

In this dissertation,applying the connection decomposition and the dual assumption, we studied the SU(2)non-Abelian gauge theory and the nonperturbative vacuum of QCD. And we also discussed the permutation group coset method in calculations of gauge field vertices.There are mainly four parts in this dissertation.In chapter one,the basic concepts of gauge field theory was introduced in brief and the study of nonperturbative field theory was reviewed.Then we described the idea of decomposition of gauge potential,which is the start point of our work.In chapter two,based on the ultraviolet/infrared scale separation of the connection decomposition variables,we proposed that at the classic level the strong-coupling limit of the Yang-Mills theory vacuum behaves as a black hole with regard to colors.With this idea,we prove that there exists a dual superconductor solution for the strongly-coupled Yang-Mills theory,whose vacuum is made up of a many-body system of magnetic charges. A dual Abelian-Higgs model,with a Higgs vacuum constant added has been derived from the gluonic field part of SU(2)QCD based on the Faddeev-Niemi decomposition and random-order assumptions.The scale potential V(φ)has the Mexico-hat form.And we calculated that the Ginzburg-Landau parameter isκ=(mφ)/(mA)=(8/9)/(1/2)(weak type-Ⅰ). This prediction is in well agreement with the result 0.85 which is consistent with recent lattice QCD simulations given by T.Sekido et al.The result predicts that the vacuum type of the nonperturbative condensate is at border between that of type-Ⅰand type-Ⅱsuperconductor.In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.In chapter four,we have studied the permutation group coset method in calculations of gauge field vertices which can simplified the calculation of gluonic vertices.Using this method we derived the Feynman rules of trilinear vertex and quartic vertex of gauge theory.