SU(3) LIMIT OF U(6/20) SUPERSYMMETRY IN NUCLEI

In this paper we discuss the SU(3) limit of U(6/20) supersymmetry. First we derive the reduction formulas of the relevant group chain. Then we discuss the dynamical symmetry. Finally we make comparison between the theoretical calculation and experimental measurement in the case of nucleus .²³⁵₉₂U₁₄₃     

SOME DISCUSSIONS ON THE SU(3)×U(1) ELECTRO-WEAK UNIFIED MODEL OF LEPTONS AND QUARKS

In this paper we discussed the following problems in the SU(3)×U(1) unified model proposed earlier: (ⅰ) Two possible choices of the Higgs fields and their comparison with the Weinberg-Salam model; (ⅱ) The form of the Higgs self potential and the realization of the spontaneous symmetry breaking; (ⅲ) The relation between the mass spectrum and the generalized Cabibbo mixing angles in a model with several generations of fermions.     

ON THE PHASE AND THE REPRESENTATION TRANSFORMATIONS OF SUn BARYON AND MESON WAVE FUNCTIONS

The baryon and meson wave functions of SU_n symmetry under the Baird-Bie-denharn phase convention are given explicitly.The phase confusion is clarified andthe matrices of transformations between I-spin,U-spin and V-spin representationsare given for the IR（8）,（27）,（35） of SU₃.     

Phase Structure of U(1) Lattice Gauge Theory by Variational Study with Independent Plaquette Effective Action

The average plaquette energy E_p of U(1) Lattice gauge theory in 3 dimensions with an independent plaquette effective action is calculated using the variational cumulant expansion.The E-β curve is continuous,which shows that U(1) theory has only one confine phase.Our result is consistent with Monte Carlo data.     

ON THE SU(4) MONOPOLE AND DYON SOLUTIONS

A simple method is proposed to obtain the classical monopole and dyon solutions in the case of SU(4) symmetry, which can be systematically generalized to the general case of SU(N). The solutions obtained in the SU(4) case correspond to magnetic charges of ±1/g,±√3/(2g),±1/(√2g).     

A VARIATIONAL METHOD IN LATTICE GAUGE THEORY BASED ON HÖLDER INTEGRAL INEQUALITY

A variational method based on Hölder integral inequality is presented. Taking the parameters in integral inequality as variational parameters, we can calculate the free energy in lattice gauge system. The plaquatte energy of Z₂ 、U(1)、 SU(2) gauge system is found and consistent with that given by Monte Carlo method. But, the higher phase transitions for U(1), SU(2) gauge systems are not found.     

U(6/20) SUPERSYMMETRY IN NUCLEI AND ITS Spin (6) LIMIT

The U(6/20) supersymmetry is discussed in this paper. Particularly we discuss its Spin (6) limit. First we discuss the reduction of the group chain of the Spin(6) limit. Secondly we derive the wave functions and excited energy formulas for the nuclei in which the Spin(6) limit of U(6/20) supersymmetry exists. Thirdly we make comparison of the nuclear energy spectra between the theoretical calculation and experimental measurement in the case of nucleus ₇₇¹⁹³Ir₁₁₆. The comparison shows that the Spin(6) limit of U(6/20) supersymmetry possibly exists in nucleus ₇₇¹⁹³Ir₁₁₆.     

DISCUSSION OF A SU(2)×U(1)×S3 MODEL WITH TWO HIGGS DOUBLETS AND CALCULATION OF CABIBBO-LIKE-PARAMETERS

In this paper a SU(2)×U(1)×S₃ model with two Higgs doublets is discussed in detail. It is shown that besides the case discussed by Segre et al., there is another physically interesting case. We investigate the latter in detail. In This case, taking the quark masses and the Cabibbo angle θ₁ as input parameters, we can obtain Cabibbo angles θ₂ and θ₃ which have the same order of magnitude as θ₁. Finally the appearance of a pseudo Goldstone boson in the model is discussed, a method to overcome the difficulty is given, and the physical results of this case which do not contradict with the experiments are discussed.     

APPROXIMATE SEQUENCE FOR U（t,t0）-OPERATOR

We give an approximate sequence for U（t,t₀）-operator.We prove the follow-ing theorems:Theorem 1.If the norm ||H（t）|| of H（t）in equation（2.1）is a Lebesgue in-tegrable function with respect to t,then there is an approximate sequence{U_n},such that for any state vector |Φ〉,|Ψ〉,the sequence <Φ|U_1^|Ψ><Φ|U_2^|Ψ>,......,<Φ|U_n^|Ψ>,......is uniform convergent with respect to t.Theorem 2.If in finite time interval,the norm ||H（t）|| of H（t）in equation （2.1）is a Lebesgue integrable function,then equation（2.1）has unique solution.     

THE PARTIALLY VIOLATED U(3) LIMITS OF THE DYNAMICAL SUPERSYMMETRY U(6/12) IN EUROPIUM-GADOLINIUM REGIONS

The partially violated U(3) limits of the U(6/12) model is presented. The theoretical predictions are compared with existing experimental data of energy spectra and B(E2). The theory tallies with experiment fairly good.     

Theoretical Analysis of an Uqp(u2) Model for Ground-State Bands in Even-Even Nuclei

The validity of an U_qp(u₂)model for the nuclear rotational spectrum is systematically analysed by investigating the Mallmann plots and fitting the experimental data for the even-even rare-earth and actinide nuclei.The results show that the theoretical values obtained from the U_qp(u₂) model are in a good accordance with the experimental findings.Thus the U_qp(u₂) model has some advantages over the SU_q(2)model as far as energy levels are concerned. Further more,a relationship between the parameters of deformations and the nuclear softness is also established.     

UNIFIED ELECTRO-WEAK MODEL IN SU (3)

In this paper a unified electro-weak model for leptons based on the SU(3) gaugegroup is suggested by means of four kinds of realization for the generators of thegroup. For all low energy electro-weak processes, this model predicts the same resultsas the conventional Weinberg-Salam model does. The Weinberg angle is shown to be sin²θ_w=1/4 in a natural way. When the Higgs self potential respects a discrete symme-try Φ→-Φ, a new conserved quantum number called weak strangeness emerges fromthe model after spontaneous symmetry breaking. In the present model there existanother four heavy vector gauge bosons V^± and U^±± together with some heavyfermions and Higgs scalars, which have non vanishing weak strangeness quantumnumbers. These weak strange particles have no direct couplings with leptons. Theirexistence will not influence the low energy electro-weak processes. Nevertheless, theycan be produced in pairs in high energy collisions and the lightest of them should bestable if the conservation of weak strangeness is exact. The experimental implicationsand the possibility of violation of the conservation of weak strangeness are also dis-cussed.     

IRREDUCIBLE REPRESENTATIONS OF THE GRADED LIE ALGEBRA SU(m/n)

Using the definition of irreducible tensor operators of the Lie group SU(n), we ive a method of calculating the irreducible representations of the graded Lie algebra U(m/n). We also give some simple examples of irreducible representations of U(3/2) and SU(m/n).     

THE REGGE TRAJECTORY OF MESONS AND THE SU(4) MASS RELATIONS

A relativistic equation of motion of a two particle system under the constraints p_i²-m_i²-U(x²)=0.(i=1,2), where U(x²) is an infinite spherical square well poten-tial, is applied to the SU(4) quark model of mesons. A set of linear mass relations areobtained. Instead of the linear relation between J and M², the Regge trajectory ob-tained is a relation between p_nl² and M², where ζ_nlπ are zeros of the spherical Besselfunctions. The new trajectory seems more satisfactory than the former one.     

AN ANALYSIS OF FOUR-ELEMENT MODELS OF LEPTONS AND NON-DIAGONAL NEUTRAL CURRENTS

Due to the possible production of neutral and charge heavy leptons by v_μ, models consisting of four elements per "line", e.g. v_e, e^-, E⁰, E^- v_μ, μ^-, M^0, M^- v_τ, τ^-, T⁰, T^- ……are analysed. Non-diagonal neutral currents cannot be avoided. Nevertheless, a model is proposed within SU_（2）×U_（1） in which the process μ→eγ can still be suppressed by the Bjorken-Lane-Weinberg mechanism; various production cross-sections for heavy leptons are reasonable when compared with experiments. Models corresponding to SU_（3）×U（1） and still higher symmetries are discussed.     

A GENERAL FORMULA ON C-G SERIES OF U(3) GRONP

As a generalization of the work [1], a general formula on C-G series of U(3)group is given. It is beautiful and effective.     

A STRUCTURE MODEL OF STRATONS AND LEPTONS

A subquark model is proposed. According to this model, stratons and leptons are consisted of rishons T and V, which are multiplets of group SU_H(3)×SU_C(3)×SU_G(2)×SU(2)×U(1). Three generations of both stratons and leptons are obtained naturally. In this model, proton decay modes are μ^－e⁺e⁺ or e^－μ⁺μ⁺.     

ON THE PROBLEM OF THE DUAL CHARGE (MAGNETIC MONOPOLE) OF NON-ABELLAN GROUPS (Ⅱ)

The method of relating the gauge potential to the connection on a spherical surface developed in a previous paper is generalized to the discussion of the potential of an SU(2) magnetic monopole with O(5) symmetry. Expressions for the potential of the monopole with double string singularity or single string singularity are obtained. Finally, by a combined coordinate-gauge transformation, we obtain a string free expression for an SU(2) magnetic monopole with O(5) symmetry.     

AN SU(4)×SU(2)×U(1) UNIFIED MODEL

In this paper we propose an SU(4)×SU(2)×U(1) unified model, in which the stratons and leptons of every generation belong to the same Multiplet, and the leptons will couple to the stratons. But this kind of coupling cannot cause the proton decay, and has only some effects in high energy scatterings. This model predicts the existense of two neutral intermediate bosons, instead of one, and the value of Weinberg angle to be sin²θ_w=0.25. The neutrinos have reasonable masses in the model.