CP(n)手征理论的非自偶解及相应的规范场

在SU(n 1)群空间里以不同方式嵌入子群SU(m)(m≤n)后,我们得到CP(n)手征场的自偶解和非自偶解。本文详细地探讨了非自偶解的来源、性质及相应的规范场与拓扑荷。现有的理论框架必然导致允许非自偶解。     

CP(n)手理论的非自偶解及相应的规范场

在SU(n+1)群空间里以不同方式嵌入子群SU(m)(m≤n)后, 我们得到CP(n)手征场的自偶解和非自偶解. 本文详细地探讨了非自偶解的来源、性质及相应的规范场与拓扑荷. 现有的理论框架必然导致允许非自偶解.     

阶化李代数SU(m/n)的不可约表示

本文利用李代数SU(n)不可约张量的概念,给出求阶化李代数SU(m/n)不可约表示的方法。并且给出SU(3/2)和SU(m/n)若干较简单的不可约表示例子。     

SU(mn)SU(m)×SU(n)单粒子母分系数

本文利用置换群CG系数计算了五个粒子以内的所有SU(mn)SU(m)×SU(n)单粒子母分系数。     

SU(mn) SU(m)×SU(n)单粒子母分系数

本文利用置换群CG系数计算了五个粒子以内的所有SU(mn) SU(m)×SU(n)单粒子母分系数.     

osp(1|4)Toda模型解的构造

将Leznov–Saveliev代数分析和Drinfeld–Sokolov构造这种方法推广到超对称情形,并运用这种方法给出osp(1|4)Toda模型的解,从而将这种方法推广到二秩情况.     

Yb原子|m|=0,1里德伯态能级Stark结构

用两步激发和光电离方法,在0-1500V/cm电场范围内,测定了Yb原子n=17至n=20附近.m=0和|m|=1的Stark光谱.采用数值积分方法对实验研究范围内的Stark能级结构作了计算,理论与实验结果基本符合.讨论了电场中能级的抗交叉行为及其与量子亏损的关系,并对m=0和|m|=1两种Stark能级结构的特点作了比较. 关键词：     

UF6分子的模型伸缩振动能级的计算

利用一个四参数非线性模型 ,对处于电子基态下的XY6型分子的X -Y键的伸缩振动进行了描述 ,并将其应用于计算UF6分子中U -F键的伸缩振动能级 .计算中引入的模型Hamilton算符所包含的描述U -F键非谐振动的参数λ和描述U -F键之间的偶极 偶极相互作用参数ε1,ε2 由实验值得出 ,波函数 |ψn〉按形式为 |n ,α〉 =|n1〉|n2 〉|n3 〉|n4〉|n5〉|n6〉的基函数集展开 ,从而把复杂的Hamilton方程转化为简单的矩阵代数方程 .结果显示 ,该非线性模型能够较好地描述UF6分子的振动 (计算误差在 1.0cm-1之内 ) ,同时合理地预测了一些至今还未观测到的能级值     

态|Ψ_n~((2))〉_q的广义非线性等阶N次方H压缩效应

构造了一种新型的多模叠加态 |Ψ(2 )n 〉q=C(R)n |{ -i Z*j }〉q+C(0 )n |{ 0 j}〉q;并首次详细地研究了此量子态的等阶 N次方 H压缩特性 .大量的计算和分析表明 :态 |Ψ(2 )n 〉q是一种多模典型的非经典光场 ;还发现了“相似压缩”等现象     

态|Ψ(2)n〉q的广义非线性等阶N次方H压缩效应

构造了一种新型的多模叠加态|Ψ(2)n〉q＝C(R)n|{-iZj}〉q+C(0)n|{0j}〉q;并首次详细地研究了此量子态的等阶N次方H压缩特性.大量的计算和分析表明:态|Ψ(2)n〉q是一种多模典型的非经典光场;还发现了"相似压缩"等现象.     

Higgs fields and the determination of the Weinberg angle

SU(2) × U(1) gauge theories, in which the Higgs fields transform as doublets under SU(2) are interpreted as pure Yang-Mills theories in six dimensions, the components of the gauge potentials in the extra dimensions playing the role of the Higgs' fields. Two consistent theories are discovered: one in which SU(2) × U(1) is embedded in SU(3) and the vector bosons remain massless - and another where SU(2) × U(1) is embedded in the graded Lie algebra SU(2|1), the symmetry is spontaneously broken in a natural fashion and the theory is equivalent to that of Weinberg and Salam, with a specific value 30° for the Weinberg angle and a prediction of the Higgs' mass.     

Gauge Field Theories on Clifford Algebras

We present a straightforward model of the U(1) gauge equations of Dirac and Maxwell, as well as the U(n) Yang–Mills equations where all fields and gauge transformations take values in a Clifford algebra. When expressed in terms of the Clifford components of the fields, the equations display various gauge symmetries which we intestigate for all Clifford algebras. In particular, for the Pauli algebra, the Dirace CA equations possess the SU(2) × U(1)-symmetry.     

Topology of the Symmetry Group of the Standard Model

We study the topological structure of thesymmetry group of the standard model, G_SM =U(1) × SU(2) × SU(3). Locally,G_SM S¹ ×(S3)² × S⁵. For SU(3), whichis an S³-bundle over S⁵ (and therefore a local product of thesespheres) we give a canonical gauge i.e., a canonical setof local trivializations. These formulas give explicitlythe matrices of SU(3) without using the Lie algebra (Gell-Mann matrices). Globally, we prove thatthe characteristic function of SU(3) is the suspensionof the Hopf map . We also study the case of SU(n) forarbitrary n, in particular the cases of SU(4), a flavor group, and of SU(5),a candidate group for grand unification. We show thatthe 2-sphere is also related to the fundamentalsymmetries of nature due to its relation to SO⁰(3, 1), the identity component of the Lorentz group, asubgroup of the symmetry group of several gauge theoriesof gravity.     

A noncommutative geometric approach to left-right symmetric weak interactions

By combining the generalized exterior algebra of forms over a noncommutative algebra with the gauging of discrete directions and the associated Higgs fields, we consider the construction of the bosonic sector of left-right symmetric models of the form SU(2) _L SU(2) _R U(1). We see that within this formalism maximal use can be made of the gauge connection associated with the noncommutative graded algebra.     

Graded gauge theory

The mathematical background for a graded extension of gauge theories is investigated. After discussing the general properties of graded Lie algebras and what may serve as a model for a graded Lie group, the graded fiber bundle is constructed. Its basis manifold is supposed to be the so-called superspace, i.e. the product of the Minkowskian space-time with the Grassmann algebra spanned by the anticommuting Lorentz spinors; the vertical subspaces tangent to the fibers are isomorphic with the graded extension of the SU(N) Lie algebra. The connection and curvature are defined then on this bundle; the two different gradings are either independent of each other, or may be unified in one common grading, which is equivalent to the choice of the spin-statistics dependence. The Yang-Mills lagrangian is investigated in the simplified case. The conformal symmetry breaking is discussed, as well as some other physical consequences of the model.     

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.     

SUPERSYMMETRIC SU(1|2) GAUDIN MODEL

In this paper, we propose a supersymmetric SU(1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.     

Vector meson masses in two-dimensional SU(NC) lattice gauge theory with massive quarks

Using an improved lattice Hamiltonian with massive Wilson quarks a variational method is applied to study the dependence of the vector meson mass Mv on the quark mass m and the Wilson parameter r in in the scaling window 1 ≤ 1/g2 ≤ 2, Mv/g is approximately linear in m, but Mv/g obviously does not depend on r (this differs from the quark condensate). Particularly for m → 0 our numerical results agree very well with Bhattacharya's analytical strong coupling result in the continuum, and the value of ((e)Mv/(e)m) |mm=0 in two-dimensional SU(NC) lattice gauge theory is very close to that in Schwinger model.     

Graded constraint algebras,OSP(1, 1|2) and superstring theory

Earlier, we have established that, for a constrained system with a first class bosonic constraint algebra, the standard BRST invariance generalizes to an OSP(1, 1|2) symmetry, with four nilpotent and anticommuting BRST-type operators. Here we generalize this to arbitrary constrained systems with a graded first class constraint algebra. Our approach is based on the Fradkin- Vilkovisky formalism and uses a relation between abelian and nonabelian constraint algebras. Subsidiary constraints and generalized structure constants play an important role in the construction. As an application, we construct the OSP(1, 1|2) generators for superstrings. Here the subsidiary constraints are identified with physically relevant operators used in the unitarity proof.     

Gauge Model Based on Group G×SU（2）

We present a model of gauge theory based on the symmetry group G×SU（2） where G is the gravitational gauge group and SU（2） is the internal group of symmetry. We employ the spacetime of four-dimensional Minkowski, endowed with spherical coordinates, and describe the gauge fields by gauge potentials. The corresponding strength field tensors are calculated and the field equations are written. A solution of these equations is obtained for the case that the gauge potentials have a particular form potentials induces a metric of Schwarzschild type on with spherical symmetry. The solution for the gravitational the gravitational gauge group space.