Canonical realizations of classical lie algebras

We construct sets of canonical realizations for all classical Lie algebras (A _n ,B _n ,C _n ,D _n ). These realizations depend ond parameters,d=1, 2, 3,...,n; all Casimir operators are realized by multiples of identity. For most of the real forms of these algebras we give sets of realizations which are, moreover, in well-defined sense skew-Hermitian. Further we study extremal cases of the presented realizations. The realizations with minimal numbers of canonical pairs are discussed from the point of view of general results concerning minimal realizations. On the other hand, a connection is found between our maximal realizations ofA _n and the Gel'fand-Kirillov Conjecture.The authors would like to thank Prof. A.Uhlmann for his kind interest in this work. They are very grateful to Prof. A. A.Kirillov and Prof. D. P.Zhelobenko for helpful discussions and to Prof. J.Dixmier for his informative letter concerning the problem mentioned in Sect. 5.One of the authors (W. L.) thanks Prof. I.Úlehla for the hospitality at the Nuclear Center of the Charles University, Praha.     

q-Oscillator realizations of the quantum superalgebrassl q (m,n) andosp q (m, 2n)

Realizations of the quantum superalgebras corresponding to theA(m, n), B(m, n), C(n+1), andD(m, n) series are given in terms of the creation and annihilation operators ofq-deformed Bose and Fermi oscillators.     

Canonical realizations of the lie algebras gl(n,R) and sl(n,R) II. Casimir operators

The eigenvalues of Casimir operators in the canonical realization of gl(n, R) and sl(n, R) presented in the first part of this paper are expressed by concrete ploynomials in parameters characterizing the realization and some of their properties are derived.     

Canonical realizations of the lie algebras gl(n, R) and sl(n, R) I. Formulae and classification

The generators of the Lie algebra of the general linear group GL(n, R) and of the special linear group SL(n, R) are, recurrently, expressed through polynomials in the quantum canonical variables p_t and q_t. These realizations are skew-Hermitian, the Casimir operations are realized by constant multiples of identity element and, in dependence on the number of the canonical pairs used, they depend on d(d?1 for sl (n,R)), d = 2, …, n, free real parameters.     

The q-boson realizations of the quantum groups U q(B n)

We give explicit realization for the quantum enveloping algebras U _q(B _n). In these formulae the generators of the algebra are expressed by means of 2n–1 canonical q-boson pairs and one auxiliary representation of U _q(B _n–1)     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.     

Canonical Representations of Sp(1,n) Associated with Representations of Sp(1)

Canonical representations of Sp(1,n) associated with finite dimensional irreducible representations of Sp(1) are defined using vector-valued Berezin kernels. Their decomposition into irreducible representations is determined by decomposing the corresponding reproducing distributions in terms of positive definite trace spherical functions on Sp(1,n). The canonical representatons are also identified with the restriction to Sp(1,n) of certain maximal degenerate representations of SL(n+1,H). Received: 1 May 1998 / Accepted: 18 November 1998     

On non-linear realizations of the groupS U(2)

The non-linear realizations of compact connected Lie groups are considered mainly from the point of view of algebraic topology. In particular, all homogeneous spaces of the groupS U(2) are listed, the construction of a few non-linear realizations ofS U(2) is given and the orbit structure of linear and non-linear realizations are discussed.On leave of absence from Research Institute for Theoretical Physics, Helsinki, Finland.On leave of absence from Institute of Physics of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia.     

Hypercomplex extensions of the general linear groupGL (n,R)

Based on the concept of quaternionic extension of general linear group, we consider the case of group extensions using generalised hypercomplex systems such as the Clifford algebra, and the Grassman algebra.     

Solvable face models related to the lie superalgebra sl(m|n)

A new series of solvable face models is presented. The Boltzmann weights are parametrized in terms of elliptic theta functions. This series generalizes the face models of type A _n ⁽¹⁾ introduced in [I].     

(n,n)-(2n, 0)碳纳米管异质结的扭转力学特性

相近直径的锯齿型和扶手椅型碳纳米管可以共轴组合形成5-7碳环交替出现的柱形对称异质结. 本文利用分子动力学方法研究了直径相近且等长锯齿型和扶手椅型碳纳米管形成的(n, n)-(2n, 0)结在扭转过程中的扭矩和轴向应力随扭转角度的变化规律以及应力传递过程. 研究发现, (n, n)-(2n, 0)结扭转应变在达弹性限度内不会产生轴向应力, 该效应对基于碳纳米管扭转特性的纳米振荡器件的设计具有重要意义.     

Measurement of cross sections for the reactions 241Am(n, 2n) and 241Am(n, 3n)

The cross sections for the reactions ²⁴¹Am(n, 2n)²⁴⁰Am and ²⁴¹Am(n, 3n)²³⁹Am are measured for several neutron-energy values in the range 13.42–14.86 MeV. An upper limit on the cross section for the reaction ²⁴¹Am(n, α)²³⁸Np is also obtained.     

Additivity and non-additivity of dissociation energies in intermolecular interactions. Theoretical studies on (H2)n,n = 2-8, (CO2)n,n = 2-6 and (HF)n,n = 2-8

CCSD(T) and MP2 results using the aug-cc-pV5Z basis set are reported for chain, cyclic and other structures of the clusters (H₂)_n, n?=?2-8, (CO₂)_n, n?=?2-6 and (HF)_n, n?=?2-8. In chain-like structures of (H₂)_n and (CO₂)_n, with the bonding type of the dimer maintained, the dissociation energy D_e of the dimer doubles for the trimer, triples for the tetramer, and so on. Due to these systems being dominated by short-range forces, interactions are essentially restricted to neighbouring monomers. For other types of (H₂)_n and (CO₂)_n structures, the multipliers relative to the dimerisation energy can be much higher. Dissociation energies for the hexamers in S₆ symmetry of both H₂ (379?cm^?1) and CO₂ (4925?cm^?1) are over ten times the respective dimerisation energies. For the chain-like trimer of HF, however, D_e is in excess of double the dimer value. Mainly due to longer-range dipolar forces, the interactions reach beyond the neighbouring monomers. The interaction energy between HF monomers in chains follows an approximate R^?2 (R being the F–F distance) relationship, The calculated dissociation energies of the HF octamer are 15,985?cm^?1 (factor of 10.4) for the chain, and 21,003?cm^?1 (factor of 13.7) for the C_6h cyclic structure.     

Investigation of (n, 2n) reactions by the evaporation process

The (n, 2n) cross sections for about 80 nuclei ranging fromA=45 to 209 were calculated using the evaporation model. The calculation was performed for incident energiesE _n which satisfy the conditionU _R =E _n +Q _n ,2n=6±1 MeV. For 11 nuclei in the above mass region, (n, 2n) excitation functions were calculated from threshold to 20 MeV. In all calculations a single set of input parameters was consistently used. The influence of the level-density parameter and neutron cross sections on the evaporation model was tested. All calculated results were compared with experimental data. The systematic discrepancy between experimental data and evaporation calculations leads to the necessity of introducing the preequilibrium emission mechanism.     

The q-boson realizations of the quantum groups Uq(B2) and Uq(C2)

We give explicit realization of formulae of canonical realization for the quantum enveloping algebrasU _q (B ₂)~U _q (so(5)) andU _q (C ₂)~U _q (sp(4)). In these formulae the generators of the algebra are expressed by means of 3 canonicalq-boson pairs and one auxiliary representation ofU _q (gl(2)).     

An experimental and quantum-chemical study of the Raman spectra and rotational isomerism of thiophosphites (RS) n PCl3 − n (R = Me, Et; n = 1, 2)

The Raman spectra of different conformations of CH₃SPCl₂, C₂H₅SPCl₂, and (C₂H₅S)₂PCl are studied within the framework of the density functional theory (B3LYP/6-31G* and B3LYP/6-31+G*) using the method of scaling of force fields. Comparison of the calculated and experimental spectra makes it possible to interpret the latter and to establish the existence of trans and gauche conformers of these molecules, which are formed due to internal rotation about the P-S and S-C bonds. This comparison also shows that, for the prediction of the degrees of depolarization of Raman lines to be correct, it is necessary to introduce diffuse functions into the basis set.     

Matrix canonical realizations of the Lie algebra o(m,n). II. Casimir operators

The matrix canonical realizations of the Lie algebra of pseudo-orthogonal group O(m, n) described in the first part of this paper are further investigated. The explicit formulae for values of the Casimir operators (which are multiples of identity in these realizations) are obtained.     

For n ≥ 5 There Is No Nontrivial Z 2-Measure on L(R n )

We prove the statement in the title. As a consequence, we note that there is no nontrivial Z ₂-measure on L(H), dim H = ∞.     

(p,n)和(p,2n)反应激发函数的系统学研究

从普朗克(Planck)黑体辐射公式和实验测量数据出发,采用唯象的方法提出了包含两个可调参量,入射质子能量从阈能到150MeV,靶核质量数在44相似文献