Casimir operators of the simplest supersymmetry superalgebras

The Casimir operators of two simplest supersymmetry superalgebras are derived. The contraction procedures by which these superalgebras and their Casimir operators can be obtained from the corresponding quantities of OSp (1, 4) are specified.     

On the tensor product of supersingleton representations ofosp(1, 2n)

The tensor product of two supersingleton representations _n of the Lie superalgebraosp (1, 2n) is studied forn2. The main results are as follows: (a) anticommutators and commutators of the odd generators in _{n n} form a skew-symmetric representation of the Lie algebrau(n, n); (b) simple explicit form of all irreducible components of _{n n}, which are labelled by a single parameterJ=0, 1, ..., has been found. Each of them is a^*-representation ofosp (1, 2n) for which assertion (a) is valid. The dimension of its vacuum subspace equals , i.e., the nondegenerate vacuum occurs for J=0 only. Basic property of this family of irreducible^*-representations of osp(1, 2n) are analogous to those of massless representations of osp(1, 4).Dedicated to Academician Václav Votruba on the occasion of his eightieth birthday.     

Elementary representations and intertwining operators for the group SU1(4)

Global realizations of all elementary induced representations (EIR) of the group SU¹(4), which is the double covering group of SO↑(5,1), are given. The Knapp-Stein intertwining operators are constructed and their harmonic analysis carried out. The invariant subspaces of the reducible EIR are introduced and the differential intertwining operators between partially equivalent EIR are defined. Invariant sequilinear forms on pairs of invariant subspaces are constructed. Differential identities between invariant sesquilinear forms on pairs of irreducible components of the reducible representations are derived. The results will be applied elsewhere to the nonpertubative analysis of Euclidean conformal invariant quantum field theory with fields of arbitrary spin.     

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.     

Eigenvalues of Casimir invariants for type I quantum superalgebras

We present the eigenvalues of the Casimir invariants for the type I quantum superalgebras on any irreducible highest weight module.     

Parabosons,parafermions, and explicit representations of infinite-dimensional algebras

The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(∞) and of the Lie superalgebra osp(1|∞). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labeled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. Alternatively, the basis vectors can be expressed as semi-standard Young tableaux.     

A remarkable connection between the representations of the Lie superalgebras osp(1, 2n) and the Lie algebras o(2n+1)

We show that there is a one-to-one correspondence between the graded representations of osp(1, 2n) and the non-spinorial representations of o(2n+1). The Clebsch-Gordan series for osp(1, 2n) reduce to the corresponding series for o(2n+1) and the properly defined Casimir operators of order at least up to four have the same eigenvalues.Supported by the Deutsche Forschungsgemeinschaft     

Supercharacters and superdimensions of irreducible representations ofB(O/s) orthosymplectic simple Lie superalgebras

The validity of different formulas in the literature for the supercharacters and superdimensions of the irreducible representations of theB(O/s) orthosymplectic simple Lie superalgebras is critically examined.     

A model for so(5) = sp(4) lie algebra

The paper is the continuation of a previous one [Physica Scripta22 (1980), 545–555] devoted to quadrupling in the shell model. We consider here a simple model of the ten- dimensional quasi-spin Lie algebra which is spectrum generating for the quadrupling Hamiltonian. The model allows us to investigate many concrete aspects of the theory of linear representations of the quasi-spin algebra. In particular, we present an explicit construction of the irreducible representation module for the finite dimensional representations, and we consider the direct product of the such irreducible modules.     

Micu-type invariants for the casimir operators of the graded Lie algebrasosp(1, 2n) application to the algebraosp(1, 4)

A method which represents a generalization of the method proposed by Micu for the construction of the Casimir operators of the Lie algebras, namely the algebrasSp(2n), is presented for the construction of the Casimir operators of higher degrees of the graded Lie algebrasosp(1, 2n). Explicite expressions for the Casimir operators are obtained for the graded Lie algebraosp(1,4).This paper appeared as a preprint of the Institute of Physics, Czechoslovak Academy of Sciences, FZU 80-1 and will be published.Abstract of the paper presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

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.     

Critical Casimir effect near the (3)He-(4)He tricritical point

We present capacitance measurements of the equilibrium thickness of (3)He-(4)He mixture films as a function of temperature and concentration. The films are adsorbed on a Cu substrate situated above bulk liquid mixture. As we scan across the tricritical point, we observe a thickening of the film indicating the presence of a repulsive critical Casimir force.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

Nonclassical representation ofosp q (1/2) algebra and completeness relation of q-deformed supercoherent states

In this paper some nonclassical representations ofosp _q (1/2) algebra are presented and the completeness relation of q-deformed supercoherent states is proved.     

1,2-二氢-4-(4-羟基苯基)(2H)二氮杂萘-1-酮的NMR研究

应用多种二维核磁共振谱,即：2D同核化学位移全相关谱(TOCSY),2D NOESY谱,2D 异核多量子相关谱(HMQC)和2D异核¹³C-¹H多键 相关谱(HMBC),对化合物1,2-二氢-4-(4-羟基苯基)(2H)二氮杂萘-1-酮的¹H和¹³C NMR 谱线进行了完整归属,从而系统地分析和讨论了该化合物的结构特征.     

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.     

Matrix elements and casimir operators of the discrete series representations of the groupU(p,q)

Explicit form of matrix elements of the discrete series representations of the groupU(p, q) are given. Casimir operators of these representations are defined.