From special unitary groups SU(2I+1) to nuclear spin statistical weights

Following a suggestion of S.R. Polo, Galbraith [J. Chem. Phys. 68 (1978) 1677] was the first to obtain nuclear spin statistical weights for molecules of the type , , and ) starting from special unitary groups. In the present contribution, an analogous but simpler method is presented allowing the calculation of nuclear spin statistical weights of rigid molecules belonging to all important molecular point groups. The molecules under consideration may contain more than one set of identical nuclei with spins up to 3. The method proposed can easily be extended to nonrigid molecules.     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.     

SU(1, 1) and SU(2) Perelomov number coherent states: algebraic approach for general systems

We study some properties of the SU(1, 1) Perelomov number coherent states. The Schrödinger's uncertainty relationship is evaluated for a position and momentum-like operators (constructed from the Lie algebra generators) in these number coherent states. It is shown that this relationship is minimized for the standard coherent states. We obtain the time evolution of the number coherent states by supposing that the Hamiltonian is proportional to the third generator K₀ of the su(1, 1) Lie algebra. Analogous results for the SU(2) Perelomov number coherent states are found. As examples, we compute the Perelomov coherent states for the pseudoharmonic oscillator and the two-dimensional isotropic harmonic oscillator.     

Exact Solutions for Self-Dual SU(2) and SU(3) Yang–Mills Fields

The (constrained) canonical reduction of four-dimensional self-dual SU(2) and SU(3) Yang–Mills theory to two-dimensional nonlinear Schrödinger (NS) and Korteweg–de Vries (KdV) equations are considered. The Bäcklund transformations (BTs) are implemented to obtain new classes of exact solutions for the reduced two-dimensional NS and KdV models.     

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.     

Configuration-mixed effective SU(3) symmetries

The procedure of Jarrio et al. (Nucl. Phys. A 528, 409 (1991)) for the determination of the effective SU(3) symmetry of nuclear states is extended to small deformations and to oblate nuclei. Self-consistency checks are carried out both for light and for heavy nuclei. Received: 23 April 2002 / Accepted: 25 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: hess@nuclear.unam.mx Communicated by A. Molinari     

群表示论的物理方法(Ⅴ)——SU3?SO3和SU4?SU2×SU2分类基

本文给出了核物理中常用的SU₃?SO₃(f=1—6)和SU₄?SU₂×SU₂波函数在Gelfand表象中的展开系数。 关键词：     

Phase structure of SU(2) and SU(3) lattice gauge theories

Using a mean field we obtain the phase diagrams for SU(2) and SU(3) with a mixed fundamental-adjoint representation action.     

SU(3) × SU(3) symmetry breaking in a simple model

A field-theoretical model, due to Lévy, is studied. It contains a triplet of quarks and a pseudoscalar and a scalar meson nonet. The original SU(3) × SU(3) symmetry is broken by terms linear in the scalar meson fields. A renormalization and regularization procedure is defined in order to remove the ultra-violet divergences. The possibility of a spontaneous breakdown of the symmetry is described and the Goldstone theorem is verified in the one-loop approximation.     

Symmetry and Similarity Solutions of a （2＋1）-Dimensional Generalized Broer-Kaup System

We study the symmetries of a （2＋1）-dimensional generalized Broer-Kaup system by means of the classical Lie group theory. The corresponding group algebra is constructed. Based on the symmetries, severaJ types of similarity solutions are obtained.     

SU(3)L × SU(3)R as gauge groups of weak and associated charges

Consequences of an SU(3)_L × SU(3)_R gauge group underlying weak-electromagnetic and associated interactions are studied. A specific pattern of symmetry breaking relates the lepton mass spectrum and mixing pattern, the effective (anti) neutrino-induced neutral current and (approximate) parity conservation in the neutral-current sector.     

Quantum Currents in the coset Space SU(2)/U(1)

We propose a rational quantum deformed nonlocal currentsin the homogeneous space SU(2)k/U(1),and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k=c is obtained.In the classical limit h→0,the quantum nonlocal currents become SU(2)k parafermion,and the realization of Yangian double becomes the parafermion realization of SU(2)k current algebra.     

The vacuum of supersymmetric SU(3) × SU(2) × U(1)

We show that in supersymmetric SU(3) × SU(2) × U(1) it is possible to break SU(2) with an Higgs singlet and at the same time to avoid vacuum expectation values for s-fermions. With rather simple constraints we obtain important restrictions on the values of the model parameters.     

Weak nonleptonic decays of 3/2+ isobars in SU(3)

Weak transitions of decuplet isobars are expanded in terms of eigen-amplitudes of the direct channel in the framework of SU(3). Starting with the most general weak Hamiltonian and assuming intermediate states to be non-exotic, we obtain ΔI=1/2 rule for Ω⁻ decays. Invoking of the CP invariance forbids all thepv weak processesD(10)→D(10) +P(8). Decays of the charmed multiplets are also discussed in these dynamical considerations. We obtain triplet dominance of charm changing weak Hamiltonian for Ω*⁺⁺ ₃ decays.     

SU(3) ⊗ SU(2) ⊗ U(1) from D = 11 supergravity

In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ? SU(2) ? U(1) as a symmetry of the internal space M₇. These solutions lead, in dimensional reduction, to SU(3) ? SU(2) ? U(1) gauge fields.In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/p which describes the embedding of the stability subgroup SU(2) ? U(1) ? U(1) of M₇ in SU(3) ? SU(2) ? U(1). For all q/p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl $\text{F}{}_{\mathrm{\alpha \beta \gamma \delta }}\text{≠ 0}$. It breaks all sypersymmetries.     

Supersymmetric extension of the SU(3)×SU(2)×U(1) model

We describe a class of supersymmetric SU(3)×SU(2)×U(1) models where all quarks and leptons, as well as their scalar partners, get masses through one-loop radiative corrections.     

Superconductivity in Restricted Chromo-Dynamics (RCD) in SU(2) and SU(3) Gauge Theories

Characterizing the dyonically condensed vacuum by the presence of two massive modes (one determining how fast the perturbative vacuum around a colour source reaches the condensation and the other giving the penetration length of colored flux) in SU(2) theory, it has been shown that due to the dynamical breaking of magnetic symmetry the vacuum of RCD acquires the properties similar to those of relativistic superconductor. Analysing the behaviour of dyons around RCD string, the solutions of classical field equations have been obtained and it has been shown that magnetic constituent of dyonic current is zero at centre of the string and also at the points far away from the string. Extending RCD in the realistic color gauge group SU(3), it has been shown that the resulting Lagrangian leads to dyonic condensation, color confinement and the superconductivity with the presence of two scalar modes and two vector modes.