SU_3U_1U_1的矢量相干态表示

本文讨论了SU_3的矢量相干态表示。利用K矩阵技术得到了SU_3?U_1?U_1的正交基矢,从而确定了权的多重度。     

SO_5SU_2SU_2U_1U_1及SO_5U_1U_1的矢量相干态表示

本文讨论了SO_5?SU_2?SU_2?U_1?U_1及SO_5?U_1?U_1的VCS表示。计算了SO_5?SU_2?SU_2的约化矩阵元,并利用K矩阵技术确定了SO_5权的多重度。     

群表示论的物理方法(Ⅳ) SU_mnSU_m×SU_n和SU_(m+n)SU_m■SU_n分类基

本文证明了置换群CG系数和外积约化系数分别就是将任一SU_m和SU_n不可约基耦合成SU_(mn)SU_m×SU_n和SU_(m+n)SU_m■SU_n分类基的耦合系数,并给出了将SU_(mn)SU_m×SU_n和SU_(m+n)SU_mSU_n分类基用Celfand基展开时计算展开系数的几种方法。给出了基本粒子中常用的SU_6SU_3×SU_2和SU_8SU_4×SU_2重子波函数。     

在SU_2格点规范理论中计算真空态胶子凝聚量

我们利用累积展开方法计算得到SU_2纯规范场理论真空态胶子凝聚量■格点规范理论提供了一个可行的计算强作用中非微扰效应的理论方案,初步计算     

群表示论的物理方法(Ⅴ) SU_3SO_3和SU_4SU_2×SU_2分类基

本文给出了核物理中常用的SU_3SO_3(f=1—6)和SU_4SU_2×SU_2波函数在Gelfand表象中的展开系数。     

一些U_NG同位标量因子的解析表达式

本文导出了部分U_6SU_3,U_N(U_1)~N及SO_7(SU_2)~3同位标量因子的解析表达式.     

对SU_3波函数的讨论

本文详细地讨论了Elliott引入的SU_3波函数Ψ(α(λμ)KLM)=2L+1/C(λμKL)integral from(xΩ(a(λμ)K)×XD_(MK)~L(Ω)dΩ)的若干性质。利用SU_3群的无穷小算子的对易关系,可以较容易地求出“内部态”波函数χ(α(λμ)K)的表达式,并由此求出了波函数Ψ(α(λμ)KLM)的母分数系数(f·p·c.)。 作为例子,本文还计算出了sd壳中有两或三个核子的SU_3波函数Ψ(α(λμ)KLM)。     

一种可能的强子结构新模型

最近在DESY和SLAC又发现了一些族粒子的新成员。当然,目前实验上还有些争议,但大体上共八个:J(3.1),'(3.7),'(4.1),'(4.4),χ(2.8),P(3.41),P(3.51),P(3.53)。这八个新粒子,能较自然地填充在我们这个新模型里。 我们假定构成强子的基础粒子总共七个:通常的SU_3三重态轻层子u,d,s和SU_4四重态重层子u′,d′,s′,c′,其中 u′,d′是同位旋二重态,电荷分别为2/3,—1/3。s′,c′均     

新粒子和层子模型理论对称性的一种可能——SU_5的扩充

在J/和′粒子发现后,SU_3难于容纳和为了解释它的性质,有人将层子模型理论的对称性从SU_3扩充到SU_4。我们不禁要问:如再发现窄共振的中性矢量介子怎么办?那时SU_4已难于容纳,其扩充的一种可能是SU_5。最近实验上确实有人宣称又发现了这种新粒子。如有人宣称发现了质量在6GeV左右且具有惊人稳定性的新粒子Υ。如     

多粒子W态的绝热制备

通过利用时间依赖的外磁场,提出了绝热制备多粒子W态的新方法.同时给出了驱动n个自旋1/2粒子从未纠缠态到W态的相互作用哈密顿量以及绝热和非绝热演化条件,展示了能量和靶态布据随时间的演化图.     

The Branching Rules for SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) and the Highest Weight States for SU(N) and O(N)

Simple analytical recurrent formulae of the branching rules for group chain SU(2N)⊃(SU(N)⊃O(N)⊃O(3))⊗SU(2) are obtained. The highest weight states for the irreducible representations [2^al^b] or {nS} of group SU(N) and for the irreducible representations (2^α1^β) or (υS) of group O(N) are constructed respectively     

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL（2, C） and the Lorentz group via the Pauli grading （the elements of SL（2, C） expressed by direct sum of unit matrix and generators of SU（2） group）, we grade the SL（3,C） group with the generators of SU（3）, i. e. the Gell-Mann matrices, then express the SU（3） group in terms of three SU（2） subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL（2,C）. If the mapping from group SL（3,C） to the Lorentz group is constructed by choosing one SU（2） subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex -γμθ^μ is extended to encompass γ5γμθ^μ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.     

超导体中库珀对的SU(2)与Glauber相干态——库珀对与约瑟夫森超流性的量子特性研究

本文利用类自旋算符证明BCS超导基态波函数是单个库珀对SU(2)相干态波函数的直积、且在一定条件下为库珀对体系的SU(2)相干态波函数。若两块处在BCS超导基态的超导体耦合在一起,则体系仍处在SU(2)相干态,且在一定条件下为定态超辐射态。在SU(2)群到谐振子群的收缩下,库珀对的SU(2)相干态变为Glauber相干态。讨论了两种情形下库珀对与约瑟夫森超流性的量子噪声、分布及二阶相关特性。     

自旋体系的一般SU(2)相干态

本文引进自旋体系的一般SU(2)相干态,讨论它的压缩特性、反聚束特性及其产生。证明当SU(2)群收缩到谐振子群时,一般SU(2)相干态转变成一般Glauber相干态,并给出有关的收缩结果。 关键词：     

Negative dimensions and E7 symmetry

The invariant length and volume which characterize the Lorentz group are extended to a quadratic and a quartic supersymmetric invariant. The symmetry group of the Grassmann sector can be SO(2), SU(2), SU(2) × SU(2) × SU(2), Sp(6), SU(6), SO(12) or E₇, which are also possible global symmetries of extended supergravities. Diophantine conditions which yield this classification follow from the corresponding conditions in d bosonic dimensions by the replacement d → ?d.     

Dynamical symmetry breaking of extended gauge symmetries

We construct asymptotically free gauge theories exhibiting dynamical breaking of the left-right gauge group G(LR)=SU(3)(c) x SU(2)(L) x SU(2)(R) x U(1)(B-L), and its extension to the Pati-Salam gauge group G(422)=SU(4)(PS) x SU(2)(L) x SU(2)(R). The models incorporate technicolor for electroweak breaking, and extended technicolor for the breaking of G(LR) and G422 and the generation of fermion masses. They include a seesaw mechanism for neutrino masses, without a grand unified theory (GUT) scale. These models explain why G(LR) and G422 break to SU(3)(c) x SU(2)(L) x U(1)(Y), and why this takes place at a scale (approximately 10(3) TeV) large compared to the electroweak scale, but much smaller than a GUT scale.     

Lorentz violation constrained by triplicity of lepton families and neutrino oscillations

In this paper we postulate an algebraic model to relate the triplet characteristic of lepton families to Lorentz violation. Inspired by the two-to-one mapping between the group SL(2, C) and the Lorentz group via the Pauli grading (the elements of SL(2, C) expressed by direct sum of unit matrix and generators of SU (2) group), we grade the SL(3, C) group with the generators of SU(3), i. e. the Gell-Mann matrices, then express the SU(3) group in terms of three SU(2) subgroups, each of which stands for a lepton species and is mapped into the proper Lorentz group as in the case of the group SL(2,C). If the mapping from group SL(3,C) to the Lorentz group is constructed by choosing one SU(2) subgroup as basis, then the other two subgroups display their impact only by one more additional generator to that of the original Lorentz group. Applying the mapping result to the Dirac equation, it is found that only when the kinetic vertex γμξμ is extended to encompass γμξμ can the Dirac-equation-form be conserved. The generalized vertex is useful in producing neutrino oscillations and mass differences.     

SU(2)群的非齐次逆微分实现

利用玻色振子的逆算符构造了SU(2)群的生成元和不可约表示的相干态,进而导出了SU(2)群的非齐次逆微分实现.     

Compensation and nonlinear theory

The existence is demonstrated of a new class of compensating fields in addition to the well-known fields of Yang-Mills type that lead to nonlinear field theory and induce a non-Euclidean geometry of spacetime. The cases of the Lorentz group, U(1), SU(2), SU(3), SU(2, 2) and coordinate transformations are considered.     

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.