【作者】 艾德臻；

【导师】 贾多杰；

【作者基本信息】 西北师范大学 ， 理论物理， 2007， 硕士

【摘要】 本论文主要运用联络分解思想和对偶超导方法来研究SU(2)非阿贝尔规范理论和QCD的非微扰真空,并讨论了利用置换群陪集简化方法来计算规范场顶角问题。主要内容分为四部分:第一章对场论的基本概念和与非微扰问题相关的研究现状作一简要介绍,并着重分析了规范势分解的提出及最近研究成果。第二章基于联络分解变量的紫外/红外分离,提出杨-米尔斯理论真空的强耦合极限表现为一个经典场论意义下色空间的黑洞,并证明在强耦合极限下该理论存在对偶超导体解,其非微扰真空可由磁荷的多粒子体系构成,借助规范场的Faddeev-Niemi分解,由SU(2)QCD的胶子部分推导出一个含有黑格斯真空常数的有效对偶阿贝尔-黑格斯模型,标量势V(Φ)具有Mexico-hat形式,计算出Ginzburg-Landau参数为κ=(mΦ)/(mA)=(8/9)/(1/2),(弱第Ⅰ类),这与最近T.Sekido等人格点QCD模拟的结果0.85很接近,进一步证实非微扰真空凝聚体在第一类和第二类超导体边界上。第三章由有效对偶阿贝尔-黑格斯模型进一步推出阿贝尔“电”场A_μ的广义对偶伦敦方程。利用不同方法求解该方程,给出了该方程的近似结果和数值模拟结果,并分别对两种情形画出图像作了比较,据此还讨论了色电场的涡旋解及能量密度,最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释,引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。第四章给出了规范场顶角计算中的置换群陪集展开方法,利用该方法可以简化胶子顶角的计算,并导出了规范场的三点及四点树图顶角的Feynman规则。更多还原

【Abstract】 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.更多还原