Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge Theory

In this paper, a general theory on unification of non-Abelian SU(N) gauge interactions and gravitationalinteractions is discussed. SU(N) gauge interactions and gravitational interactions are formulated on the similar basisand are unified in a semi-direct product group GSU(N). Based on this model, we can discuss unification of fundamentalinteractions of Nature.     

SU(3) Local Gauge Field Theory as Effective Dynamics of Composite Gluons

The effective dynamics of quarks is described by a nonperturbatively regularized NJL model equation with canonical quantization and probability interpretation. The quantum theory of this model is formulated in functional space and the gluons are considered as relativistic bound states of colored quark-antiquark pairs. Their wave functions are calculated as eigenstates of hardcore equations, and their effective dynamics is derived by weak mapping in functional space. This leads to the phenomenological SU(3) gauge invariant gluon equations in functional formulation, i.e., the local gauge symmetry is a dynamical effect resulting from the dynamics of the quark model.     

Self-Dual Solutions for SU(2) and SU(3) Gauge Fields on Euclidean Space

Self-dual solutions for SU(2) gauge fields on Euclidean space that satisfy Yang's ansatz are generalized by considering as a function of for a special case when is a complex analytic function and for SU(3) when _i, i = 1, 2, 3, are complex analytic functions.     

2+1维SU(3)格点纯规范场的真空态计算

用连续极限截断的格点本征值方法^[1],研究2+1维SU(3)的格点规范理论的真空态.在强耦合区,上述方法的结果与强耦合展开一致.在过渡区,上述方法的结果显示出较好的标度行为.     

Gravitating Dyons and Dyonic Black Holes in SU(2) and SU(5) Theories

The study of gravitating dyons and dyonic black holes in SU(2) and SU(5) theories has been undertaken and it has been shown that gravitating fundamental dyonic solutions and dyonic black holes are stable in both the cases.     

SU(2)纯格点规范场热力学非对称点阵Monte-Carlo模拟

在非对称点阵(ξ=2,3)上模拟了SU(2)纯格点规范场系统的热力学行为,结果表明,非对称点阵Monte-Carlo模拟是实现快速趋向连续物理极限的有效途径.     

Vector and Spinor Decomposition of SU（2） Gauge Potential, Their Equivalence, and Knot Structure in SU（2） Chern-Simons Theory

In this paper, spinor and vector decompositions of SU（2） gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear 0（3） sigma model from the SU（2） mass/ve gauge field theory, which is proposed according to the gauge invariant principle. At last, the knot structure in SU（2） Chern-Simons filed theory is discussed in terms of the Φ-mapping topological current theory, The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of Φ-mapping.     

SO(n)规范势的可分解理论

使用几何代数方法,研究了n维紧致黎曼流形上SO(n)规范势(自旋联络)的一般分解理论,建立了SO(n)规范场用球丛上单位矢量场n分解的一般表达式.由此,分别得到了U(1)规范场和U(2)规范场用单位矢量场n分解的一般形式.     

量子体系的相空间规范变换

外尔于1918年引入的规范变换实际上是相位变换而非真正的尺度变换,但规范不变性、规范理论等概念都沿袭了下来。我们发现,针对由量子化条件[x, p]=iℏ而来的量子体系之本征值问题存在规范变换,或者说尺度变换,x → x/α,p → αp,该变换保体系的能量谱不变。量子谐振子、氢原子问题及一类多体问题的精确解析解证实了这一点。量子化条件 [x, p]=iℏ看来是个对量子力学很强的约束,不止于能量的量子化。这个规范变换提醒我们相空间的体积及其量子化才是物理的关键,这也是量子力学和统计物理在潜意识里一直沿用却未予关注的思路。有趣的是,从量子谐振子体系的相空间表述似乎不能导向这个结论。如同规范理论所断言的电磁学量在给定坐标系下的数值表征与标度无关,我们认为量子体系的物理量,如能量谱等,在给定坐标系下的数值表征亦应与标度无关。此尺度变换与德布罗意关系相恰。     

Obtaining the Gauge Invariant Kinetic Term for a SU(n) U ⊗ SU(m) V Lagrangian

We propose a generalized way to formally obtain the gauge invariance of the kinetic part of a field Lagrangian over which a gauge transformation ruled by an SU(n) _U ⊗ SU(m) _V coupling symmetry is applied. As an illustrative example, we employ such a formal construction for reproducing the standard model Lagrangian. This generalized formulation is supposed to contribute for initiating the study of gauge transformation applied to generalized SU(n) _U ⊗ SU(m) _V symmetries as well as for complementing an introductory study of the standard model of elementary particles.     

2+1维SU(2)格点规范场真空态的研究

对2+1维SU(2)格点规范场论真空态进行研究,推导出连续极限下真空波函数中参数μ₀和μ₂的普适表达式.并用基于改进的哈密顿量的截断本征方程进行数值计算,结果在深度弱耦合区内显示出良好的标度行为.     

（2十1）维SU（2）格点规范场胶球质量的解析计算

从连接图方案出发，计算０胶球质量，得到较好的标度行为．     

SU(2)规范场分解与Bose-Einstein凝聚体中的环流条件

利用SU(2)规范场的单位矢量场分解形式讨论了Bose-Einstein凝聚体中的环流条件.对于二分量Bose-Einstein凝聚,内部态的SU(2)对称性将导致一个拓扑环流条件,这是一个推广的Mer-min—Ho关系.     

2+1维SU(2)规范场真空波函数的研究

利用强耦合展开和本征函数以及变分方法研究了真空波函数，将这些结果进行了比较．     

The Mass Gap of SU(2) Lattice Gauge Theory in 2+1 Dimensions

Coupled cluster expansions are applied to study the eigenvalue problem of the Hamiltonian lattice gauge theory with the orthogonal D-loop basis being used to expand wavefunctions. The 0⁺⁺ bound state wavefunction and its mass gap relative to the vacuum of SU(2) lattice gauge theory in 2+1 dimensions are calculated up to the 7th order.     

On a Mathematical Definition of a Renormalization Transformation for Lattice Gauge Theories

In lattice gauge theories, the renormalization transformation and its properties are formally defined and formally proved by making use of Dirac's function and its properties. In this Letter, we shall give a mathematically rigorous definition of a renormalization transformation for lattice pure gauge field theories and show the required properties, which are use to show ultraviolet stability of lattice gauge theories.     

2维SU(NC)格点规范理论中夸克真空凝聚

用改进的Wilson夸克格点哈密顿量和变分法研究2维SU(N_C)规范场中夸克真空凝聚〈ψψ〉与夸克质量m_q和Wilson参数r的依赖关系. 结果表明: 对于给定的r, 当N_C=2,3,4,5,6,7,时, 〈ψψ〉_suba/(gN_C^3/2)的值随m_q的增大而减小. 对于较大的N_C(如N_C>3), 当m_q很小时, 〈ψψ〉_suba(gN_C^3/2)对r的依赖性很小, 但随着m_q的增大, 〈ψψ〉_suba/(gN_C^3/2)对r的依赖性增大, 且〈ψψ〉_suba/(gN_C^3/2)的值随r的增大而增大; 特别是, 当m_q→0时, 本文的格点结果与Zhitnitsky的连续理论分析结果(在弱耦合相中)很好地一致, 这意味着本文在m_q≠0时所得到的结果是可靠的.     

用改进的格点哈密顿量计算2+1维SU(2)规范场胶球质量

用改进的格点哈密顿量和截断本征方程法计算2+1维SU(2)规范场胶球质量,结果在广阔的耦合区内(1.0≤1/g²≤8.0)显示出极好的标度行为.