The Ricci tensor of SU(3)-manifolds

Following the approach of Bryant [R. Bryant, Some remarks on G₂-structures. e-print: math.DG/0305124] we study the intrinsic torsion of a SU(3)-manifold deriving a number of formulae for the Ricci and the scalar curvature in terms of torsion forms. As a consequence we prove that in some special cases the Einstein condition forces the vanishing of the intrinsic torsion.     

Matrix elements of tensor operators

The Wigner-Eckart theorem for matrix elements of tensor operators transforming according to a finite-dimensional representation of a non-compact semisimple Lie group is proved. The applications of this theorem are discussed.     

On the structure of the microscopic dielectric tensor in incommensurate crystals

A microscopic model for calculating the optical response of incommensurately modulated phases in insulating crystals is presented. The dominant contribution to the dielectric permittivity tensor is shown to originate from the lowest-index reciprocal lattice vectors, thus proving the validity of the mesoscopic approach developed in several earlier studies. The expression for the mesoscopic Fourier component of the dielectric tensor is obtained. These results may be useful in relation to the controversial problem of the optical activity observed in the incommensurate phases of some A₂BX₄ family crystals.     

On the SU(3) Mass Formulae

It is found that in the SU(3) broken quark model the SU(3) generators and their time derivatives belong to the SU(3) × SU(3) algebra. Using this algebra and the infinite momentum method the SU(3) mass sum rules are obtained. The possibility is discussed that normal spin-parity nonets and anomalous ones differ in the structure of the mass spectrum.     

On the quantization of SU(3) skyrmions

The quantization condition derived previously for SU(2) solitons quantized with SU(3) collective coordinates is generalized for SU(3) skyrmions with nonzero strangeness content. Quantization of the recently discovered dipole-type configuration with large strangeness content is considered as an example. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 6, 391–396 (25 September 1996) This study was supported by the Russian Fund for Fundamental Research, Grant 95-02-03868a and by Volkswagenstiftung, FRG. Published in English in the original Russian journal. Edited by Steve Torstveit.     

On the Wigner-Eckart theorem for tensor operators connected with compact matrix quantum groups

In this Letter, the notion of a tensor operator connected with a unitary, smooth, finite-dimensional representation of a compact, matrix quantum group is introduced and investigated. It is proved that, for compact matrix, simply reducible quantum groups, there exists a theorem analogous to the famous Wigner-Eckart theorem.     

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.     

Topological structure of the solitons solution in SU（3） Dunne-Jackiw-Pi-Trugenberger model

By using C-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU（N） Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU（3） case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of C-mapping. In our solution, the flux of this soliton is naturally quantized.     

Topological structure of the solitons solution in SU(3) Dunne-Jackiw-Pi-Trugenberger model

By using φ-mapping topological current theory and gauge potential decomposition, we discuss the self-dual equation and its solution in the SU(N) Dunne-Jackiw-Pi-Trugenberger model and obtain a new concrete self-dual equation with a δ function. For the SU(3) case, we obtain a new self-duality solution and find the relationship between the soliton solution and topological number which is determined by the Hopf index and Brouwer degree of φ-mapping. In our solution, the flux of this soliton is naturally quantized.     

A pattern calculus for tensor operators in the unitary groups

For a large class of tensor operators inU(n), a surprisingly simple diagrammatic calculus of patterns is shown to exist; to each operator of this class a pattern may be assigned in terms of which thecomplete algebraic formula for all matrix elements may be read off directly. The class of operators includes all fundamental, elementary and extremal Wigner operators in allU(n). Application of the pattern calculus toward the explicit determination of all tensor operators is discussed.Supported in part by the U. S. Army Research Office (Durham), the National Science Foundation, and the U.S. Atomic Energy Commission.     

The phase structure of the SU(3) lattice gauge-Higgs model

The phase structure of SU(3) symmetric gauge-Higgs theory with a fluctuating radial mode is investigated. The Higgs fields are considered in the fundamental representation of SU(3). It is shown that the phase structures of SU(3) and SU(2) symmetric models coincide qualitatively.     

On the structure of the algebra of field operators. II

The global structure analysis of local field operators is reinvestigated.     

Anomalous dimensions of tensor operators in 4−ϵ dimensions

Anomalous dimensions of tensor operators that determine the Callan-Gross and Corwall-Norton sum rules for the deep inelastic structure functions are calculated to first order in ? in the pseudoscalar Yukawa coupling model. Their values are found to be intermediate between those for the φ⁴ model and the gluon model.     

SU(3) symmetry for orbital angular momentum and method of extremal projection operators

Basic elements of the formalism of the theory that is based on the representations of the SU(3) group for the case of its reduction to the SO(3) subgroup of orbital angular momentum and which is widely used in theoretical physics is presented in a systematic and consistent form. Irreducible SU(3) ? SO(3) bases, both a nonorthogonal one chosen among Elliott vectors and an orthogonal one obtained from a nonorthogonal one by diagonalizing the Bargmann-Moshinsky operator, are described in detail. In particular, it is shown that there is wide arbitrariness in choosing a basis among Elliott vectors. The SU(3) ? SO(3) Clebsch-Gordan coefficients are considered in detail, along with all of their classical symmetry properties. A brief survey (history of discovery) of the method of extremal projection operators for Lie symmetries (Lie algebras and superalgebras and their quantum analogs) is given.     

The effect of tensor correlations on isovector operators

Very simple relations between renormalization factors and corrections to the GT-type-decay operator, isovector magnetic moment and coulomb energy differences between mirror nuclei due to tensor correlations are obtained.     

The effect of tensor correlations on isovector operators

Very simple relations between renormalization factors and corrections to the GT-typeΒ-decay operator, isovector magnetic moment and coulomb energy differences between mirror nuclei due to tensor correlations are obtained.