SU_4群与基本粒子的对称性

从李羣的一般理论,具体地讨论了SU_4的数学处理,给出了羣的代数结构、不可约表示维数的公式、三个基本表示的明显形式及表示直积分解的主要结果。根据SU_4对称,下列基本粒子的对称模型被构成:(1)Bacry和Van Hove模型,(2)Schwinger模型,(3)正反粒子对称的坂田模型,(4)正反粒子对称的八度法模型。在这些模型中,一些与实验一致的新的结果被得到。     

SU3羣不可约表示直乘的分解

本文利用SU₃羣无穷小算子的对易关系,求出了SU₃羣的所有不可约U表示,并导出了SU₃羣的约化系数满足的方程。作为例子,我们计算了SU₃羣的(01)×(10),(11)×(10),(11)×(11),(30)×(11)的约化系数。     

奇异粒子非轻子衰变的选择定则

本文用SU₃和G₂羣讨论了奇异粒子非轻子衰变的弱作用的变换性质。若强作用是SU₃对称的,可引进类似于同位旋(T旋)的V旋和U旋,和T旋一起来表示奇子非轻子衰变的选择定则。求得了简单选择定则情况下各个衰变过程的关系,其中包含了前人的结果而避免引用过多的假设。若强作用是G₂对称的,可引进包含同位旋在内的六种“旋”来给出选择定则。根据这些定则求得若干衰变过程的关系。证明了弱作用不能按G₂羣的七维或十四维表示变换。     

SU6(1)×SU3(2)模型及SU8模型中强子的次强质量分裂和新粒子的质量关系

新发现的J(3100)及ψ(3700)粒子可能可以按SU₆⁽¹⁾×SU₃⁽²⁾模型或SU₈模型分类。本文用引进等效层子次强作用的方法,研究这两个模型中多重态的次强质量分裂,得到了一系列有新自由度的粒子的质量关系。由于本文对等效层子作用的具体形式未作没有太大根据的取舍,所以,结果与模型的关系比较直接。本工作的结果还表明,完全可以用一个统一的等效层子作用去描写重子及介子的次强质量分裂,而不与现有的实验值冲突。     

量子代数SUq(4)的不可约表示

本文利用类张量的方法计算了量子代数SU_q(4)在SU_q(4)>SU_q(2)+SU_q(2)基上的不可约表示,得到了求矩阵元的递推公式.     

相对论层子模型中的介子和重子波函数

本文从层子模型的基本假定出发,对介子和重子波函数进行了探讨。文中讨论了介子、重子这样的强耦合束缚态的物理特性,指出“层子对”的产生效应对波函数的贡献是重要的。文中给出了具有任意角动量的介子波函数的一般形式。在质心系中,假定介子波函数和重子波函数具有近似的SU₆对称性质,得到了在质心系具有SU₆对称性质的介子波函数和基态重子波函数的一般形式,禁戒了实验中不出现的介子态。在质心系假定了O₃?SU₆对称性,写下了在质心系具有这种对称性的几个低激发态重子的波函数。在每一个O₃?SU₆多重态中的介子和重子波函数都含有两个洛仑兹协变的空间函数,对强耦合的束缚态,由于“层子对”的产生效应是重要的,这两个不变函数一般是不相等的。由于只在质心系假定了SU₆和O₃?SU₆对称,因而可以使波函数具有洛仑兹协变性,即运动系中这种对称性是不存在的。     

球对称的SU2规范场和磁单极的规范场描述

本文讨论球对称的SU₂规范场,证明了满足最一般的球对称定义的SU₂规范场只能有三种基本类型:(1)同步球对称规范场;(2)狭义球对称规范场;(3)化约为U₁子群的球对称规范场。文中详细讨论了球对称的带同位旋向量场(Higgs场)的SU₂规范场,完全决定了它们的类型。如果把这种场看成为由电磁场和带电矢介子构成,那末就有如下的结论:如果磁单极所含的磁荷是最小单位的m倍,当|m|>1时,球对称的带Higgs场的SU₂规范场只能是纯电磁场,而不能有带电矢介子场出现。但当m=0,±1时,球对称的带电矢介子场是可以出现的。从而可见,具有非单位磁荷的磁单极隐含了某种破坏球对称的因素。     

群表示论的物理方法(Ⅳ)——SUmn?SUm×SUn和SUm+n?SUm?SUn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_m?SU_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SU₆?SU₃×SU₂和SU₈?SU₄×SU₂重子波函数。     

IBM4中的强耦合SU(3)极限

将IBM推广应用于轻核时收IBM4.本文讨论了其中的下述群链.U(36)U₆(sd)×U₆(ST) SU₃(sd)×SU₃(S)×SU₃(T) SU₃(sdS)×SU₃(T)× O₃(J)× O₃(T)的约化、典型能说与E2跃迁,并用它对sd壳的核基态进行了分类.     

B2羣与奇异粒子轻子型衰变

在超荷-电荷表象中应用B₂羣对称性讨论了基本粒子的轻子型衰变。将重子和介子分别填充在B₂羣的4维表示时,在10维(正则)表示中正好包含所有|ΔS|≤1和|ΔQ|≤1的重子流或介子流。假定弱相互作用由中间玻色子作媒介,并将它们纳入B₂羣的10维表示中,计算了包括ΔS=+ΔQ和ΔS=-ΔQ两类过程的各种奇异粒子轻子型衰变几率。结果与现有实验材料不矛盾。     

A remark on SU4

Several of the interesting new relations in elementary particle physics discovered from the hypothesis of SU₆ symmetry of strong interactions, are shown to follow from the less restrictive assumption of SU₄ symmetry alone. Since isospin invariance is a much more closely obeyed symmetry than SU₃, these relations may be the best tests for the validity of combining internal symmetries with spin.     

Dynamical fermion mass hierarchy and flavour mixing

The chiral symmetry breaking of high colour representations produces dynamical breaking of the standard electroweak gauge symmetry. By enlarging the colour group and subsequently breaking it down toSU(3) _c fermions acquire radiative masses from the chiral breaking. We present attempts to produce realistic fermion mass matrix in two classes of models depending on the way that the colour group is enlarged. A realistic example is found in one of these classes of models.     

Two-Dimensional Quantum Hamiltonians with Shape Invariance Symmetry

It is shown that the Casimir operator associated with the U(1) Lie derivative defined on the S ²=SU(2)/U(1) base manifold, can be interpreted as Hamiltonians of a pair of scalar particle and scalar anti-particle with opposite charges over the S ² manifold in the presence of a magnetic monopole located at its origin and an external electric field. Using the SU(2) representation, the spectra of these Hamiltonians have been obtained. It is also proved that these Hamiltonians are isospectral and having the shape invariance symmetry, i.e. they are supersymmetric partner of each other. Also the Dirac’s quantization of magnetic charge comes very naturally from the finiteness of the SU(2) representation.     

B2羣和基本粒子强相互作用

计算了B₂羣不可约表示的直接乘积4×4,4×5,4×10和5×5分解中的约化系数。给出了它在基本粒子强相互作用对称性方面的应用的若干例子:推导了散射截面关系和低维数表示的质量关系,讨论了共振态的填充和衰变情况以及R反演不变性等。     

Higgs mechanism without Higgs particle

Until now there has been no empirical evidence for the existence of the Higgs particle, although the Higgs mechanism of symmetry breaking is very successful. We propose a scalar-tensor theory of gravity with the Higgs field of theSU(3)×SU(2)×U(1) standard model of the elementary particles as scalar field, which results finally in Einstein's gravity and in theSU(3)×SU(2)×U(1) standard model without any influence of the excited Higgs field.     

Flavon inflation

We propose an entirely new class of particle physics models of inflation based on the phase transition associated with the spontaneous breaking of family symmetry responsible for the generation of the effective quark and lepton Yukawa couplings. We show that the Higgs fields responsible for the breaking of family symmetry, called flavons, are natural candidates for the inflaton field in new inflation, or the waterfall fields in hybrid inflation. This opens up a rich vein of possibilities for inflation, all linked to the physics of flavour, with interesting cosmological and phenomenological implications. Out of these, we discuss two examples which realise flavon inflation: a model of new inflation based on the discrete non-Abelian family symmetry group A₄$A_4$ or Δ₂₇${\mathrm{\Delta }}_{27}$, and a model of hybrid inflation embedded in an existing flavour model with a continuous SU(3)$\mathit{SU}(3)$ family symmetry. With the inflation scale and family symmetry breaking scale below the Grand Unification Theory (GUT) scale, these classes of models are free of the monopole (and similar) problems which are often associated with the GUT phase transition.     

On some geometrical consequences of physical symmetries

It is shown that there exists only one submanifold O^(4,m)₂ of the representation space C^4m of the group GL(4,C)×GL(m,C) which admits a unique projection onto Minkowski space, consistent with the group. We describe the decomposition of this manifold O^4,m)₂ when the group is restricted to the physical symmetry group SU (2,2)× ×SU(m) or P×SU(m). We consider also representations of SU(2,2)×SU(m) in the resulting submanifolds and in the Hilbert space of functions over these manifolds.     

A systematic search for a realistic SU(n) tumbling gauge model

Within the framework of the dynamical symmetry breaking and the tumbling ideas, a systematic search was carried out in SU(n) groups with the ultimate aim of determining if a realistic and phenomenologically acceptable model exists which tumbles down to SU(3)_c ? U(1), or a suitable large group. To do so all the anomaly free and the asymptotically free fermion contents for any SU(n) were first determined. In order to have nontrivial tumbling the real and the pseudo-real representations have been eliminated, and the tumbling patterns of all the allowed complex ones in detail have been examined. No such realistic model has been found. These results combined with those of Srednicki's concerning the SO(4n + 2) and E₆ groups establish the fact that there cannot be any realistic tumbling gauge model within the context of the original tumbling hypotheses. Having thus established the need for a change of these hypotheses some suggestions and comment on various ways of remedying the problem are made.     

Two dimensional gases of weight charges and SU(N) fermino theories

We analyze two dimensional gases composed of particles interacting via a Coulomb or Yakawa potential through their “non-Abelian” charges. These charges are taken to be elementary weight or root vectors of SU(N). The grand partition function of these gases is shown to be equivalent to the generating functional of sine-Gordon models with weight vectors and hence to that of SU(N) fermion models. The fermion field creates or annihilates topological solitons which have elementary weight vectors as topological quantum numbers. Then, we discuss the confinement of fermions in the SU(N) Higgs models, where instantons (Z_N vortices) constitute a Yukawa gas of weight charges. We prove that fermions are confirmed by the effects of instantons in the SU(N) Higgs models in contrast with the Abelian Higgs model.