and as Vertex Operator Extensions¶of Dual Affine Algebras

We discover a realisation of the affine Lie superalgebra and of the exceptional affine superalgebra as vertex operator extensions of two algebras with “dual” levels (and an auxiliary level-1 algebra). The duality relation between the levels is . We construct the representation of on a sum of tensor products of , , and modules and decompose it into a direct sum over the spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to is traced to the properties of embeddings into and their relation with the dual pairs. Conversely, we show how the representations are constructed from representations. Received: 29 July 1999 / Accepted: 6 February 2000     

Dorey’s Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

Let \({U_q(\widehat{\mathfrak g})}\) be the quantum affine algebra associated to a simply-laced simple Lie algebra \({\mathfrak{g}}\) . We examine the relationship between Dorey’s rule, which is a geometrical statement about Coxeter orbits of \({\mathfrak{g}}\) -weights, and the structure of q-characters of fundamental representations V _i,a of \({U_q(\widehat{\mathfrak g})}\) . In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and sufficient condition for the monomial 1 to appear in the q-character of a three-fold tensor product \({V_{i,a}\otimes V_{j,b}\otimes V_{k,c}}\) .     

High-Resolution Spectroscopy of Jet-Cooled (32)SO(2) and (34)SO(2): The ã(3)B(1)-;X(1)A(1), 2(1)(0) and 1(1)(0) Bands

Laser-induced excitation spectra of the two bands ?(3)B(1)-;X(1)A(1), 2(1)(0) and 1(1)(0) of (32)SO(2) and (34)SO(2) have been recorded in a supersonic jet at a resolution of 0.015 cm(-1). The rotational and electron-spin fine structure has been analyzed for both isotopic species. Analysis of the rotational and electron-spin fine structure yields precise values of the rotational constants A, B, and C and the spin constants alpha and beta for both (32)SO(2) and (34)SO(2) in the states ?(3)B(1) (010) and (100). No interaction between these two vibrational states with any nearby triplet state is observed for rotational levels with J 相似文献   

Cλ-Extended Oscillator Algebras and Some of Their Deformations and Applications to Quantum Mechanics

C-extended oscillator algebras generalizing the Calogero—Vasiliev algebra,where C is the cyclic group of order , are studied both from mathematical andapplied viewpoints. Casimir operators of the algebras are obtained and used toprovide a complete classification of their unitary irreducible representations underthe assumption that the number operator spectrum is nondegenerate. Deformedalgebras admitting Casimir operators analogous to those of their undeformedcounterparts are looked for, yielding three new algebraic structures. One of themincludes the Brzezi´nski et al. deformation of the Calogero—Vasiliev algebra as aspecial case. In its bosonic Fock-space representation, the realization ofC-extended oscillator algebras as generalized deformed oscillator ones is shown toprovide a bosonization of several variants of supersymmetric quantum mechanics:parasupersymmetric quantum mechanics of order p = – 1 for any , as wellas pseudosupersymmetric and orthosupersymmetric quantum mechanics of ordertwo for = 3.     

(2+1) Newton�CHooke Classical and Quantum Systems

We study the Newton?CHooke groups in (2+1)-dimensions. A complete classification of both classical and quantum elementary systems is achieved by explicit computation of coadjoint orbits and unitary irreducible representations of the extended (by central extensions) Newton?CHooke groups. In addition, we show the quantization à la Moyal of a classical system using the Stratonovich?CWeyl correspondence. An analysis of the origin of the ??exotic?? central extension, which only appears in (2+1)-dimensions, is presented.     

Quantum groupSU(1, 1) ⋊ Z2 and “super-tensor” products

A quantum analogue of the groupSU(1,1)Z ₂—the normalizer ofSU(1, 1) inSL ₂(C)—is introduced and studied. Although there isno correctly defined tensor product in the category of *-representations of the quantum algebraC[SU(1, 1)] _q of regular functions, some categories of *-representations ofC[SU(1, 1)Z ₂] _q turn out to be endowed with a certainZ ₂-graded structure which can be considered as a super-generalization of the monoidal category structure. This quantum effect may be considered as a step to understanding the concept of quantum topological locally compact group.In fact, there seems to be afamily of quantum groupsSU(1, 1)Z ₂ parameterized by unitary characters T ¹ of the fundamental group of the two-dimensional symplectic leaf ofSU(1, 1)/T, whereT is the subgroup of diagonal matrices.It is shown that thequasi-classical analogues of the results of the paper are connected with the decomposition of Schubert cells of the flag manifoldSL ₂(C)_R/B (whereB is the Borel subgroup of upper-triangular matrices) into symplectic leaves.Supported by the Rosenbaum Fellowship.     

Nahm Transform for Periodic Monopoles¶and ?=2 Super Yang–Mills Theory

We study Bogomolny equations on ℝ²×?¹. Although they do not admit nontrivial finite-energy solutions, we show that there are interesting infinite-energy solutions with Higgs field growing logarithmically at infinity. We call these solutions periodic monopoles. Using the Nahm transform, we show that periodic monopoles are in one-to-one correspondence with solutions of Hitchin equations on a cylinder with Higgs field growing exponentially at infinity. The moduli spaces of periodic monopoles belong to a novel class of hyperk?hler manifolds and have applications to quantum gauge theory and string theory. For example, we show that the moduli space of k periodic monopoles provides the exact solution of ?=2 super Yang–Mills theory with gauge group SU(k) compactified on a circle of arbitrary radius. Received: 20 July 2000 / Accepted: 29 November 2000     

Conformal Affine Toda Fields on Loop Algebra:A2^(2) Case

By studying the A2^(2) Toda model based on the twist affine algebra A2^(2),we obtained the conformal-invariant porperty of the A2^(2) Toda equation.Furthermore we presented the classical r-matrix that satisfies the Yang-Baxter equation.     

On the Finite-Dimensional Quantum Group M3⊕(M2|1(Λ2))0

We describe a few properties of the nonsemisimple associative algebra =M₃ (M_2|1 (²))₀, where ² is the Grassmann algebra with two generators. We show that is not only a finite-dimensional algebra but also a (noncommutative) Hopf algebra, hence a finite-dimensional quantum group. By selecting a system of explicit generators, we show how it is related with the quantum enveloping of SL_q(2) when the parameter q is a cubic root of unity. We describe its indecomposable projective representations as well as the irreducible ones. We also comment about the relation between this object and the theory of modular representation of the group SL(2, F₃), i.e. the binary tetrahedral group. Finally, we briefly discuss its relation with the Lorentz group and, as already suggested by A.~Connes, make a few comments about the possible use of this algebra in a modification of the Standard Model of particle physics (the unitary group of the semisimple algebra associated with is U(3) × U(2) × U(1)).     

Baxter’s Q-operators and Operatorial Bäcklund Flow for Quantum (Super)-Spin Chains

We propose the operatorial Baxter’s TQ-relations in a general form of the operatorial Bäcklund flow describing the nesting process for the inhomogeneous rational gl(K|M) quantum (super)spin chains with twisted periodic boundary conditions. The full set of Q-operators and T-operators on all levels of nesting is explicitly defined. The results are based on a generalization of the identities among the group characters and their group co-derivatives with respect to the twist matrix, found by one of the authors Kazakov and Vieira (JHEP 0810:050, 2008). Our formalism, based on this new “master” identity, allows a systematic and rather straightforward derivation of the whole set of nested Bethe ansatz equations for the spectrum of quantum integrable spin chains, starting from the R-matrix.     

铁电单晶(K_xNa_(1-x))_(0.4)(Sr_yBa_(1-y))_(0.8)Nb_2O_6的光学性质和线性电光效应

本文介绍铁电单晶(K_xNa_(1-x))_(0.4)(Sr_yBa_(1-y))_(0.8)Nb_2O_6的光学性质和线性电光效应的测量。实验结果表明,这种晶体具有较大的光学双折射,透光范围由4000A到5.6μm。晶体具有低的线性电光调制的半波电压,其电光调制价值指数n_0~3·γ_c高达730×10~(-12)m/V,而激光损伤阈值为600MW/cm~2(4 pps),表明该晶体可作为较大功率激光调制使用的材料。     

Multimode q-Oscillator Algebras with q2(k+1) = 1 and Their Bargmann–Fock Representations

A countably infinite class of multimode q-oscillator algebrasA _k;m (k = 1, 2, ..., m = 1, 2, ...) is obtained with the aid of the R-matrix method in quantumgroup theory for q ^2(k+1) = 1. The related Fock spaces are given and they showthat the q-particle systems described by A _k;m obey a generalized Pauli exclusionprinciple. The algebras A _k;m are represented on a kind of q-holomorphic functionspaces B(¯) _k;m which are generalizations of the usual Bargmann–Fock spaceswith many Grassmann variables and have Hilbert space structures with the scalarproduct given by an algebraically defined integral. When taking k = 1 or k , all of the above are reduced to the corresponding results for the usual multimodefermion and boson systems, respectively.     

Toroidal Braid Group Action and an Automorphism of Toroidal Algebra Uq(sln+1,tor) (n ≥ 2)

Utilizing an action of a modification of the double affine Hecke braid group of type gl_n+1, we obtain an automorphism of the toroidal algebra U_q(sl_n+1) (n 2), which maps two central elements C and k₀ · k_n to k₀ · k_n and C^–1, respectively.     

Chemical adsorption of C60 on diamond (100)(2×1) surfaces

Molecular-dynamics simulations (MDSs) and ab initiocalculations are used to investigate the adsorption behavior of C₆₀ molecules on a clean dimer-reconstructed (100)(2×1) diamond surface. C₆₀ molecules have some probability to be adsorbed on the diamond surface at low incident energy (6∼45 eV). Electron-density contours show strong chemical interaction between C₆₀ molecules and the substrate surface. The adsorption property depends strongly on the incident energy and the impacting point. An incident energy of 18 eV may be an appropriate energy to grow a sub-monolayer or monolayer C₆₀ film on a clean C(100)(2×1) surface at room temperature. Received: 5 July 2000 / Accepted: 17 October 2000 / Published online: 28 February 2001     

Entanglement and Quantity in Quantum Space-- About Quantum Measurement (Ⅱ)

As a continuation and extension of "quantity in phase space" "quantity in quantum space" is introduced. With that, the disappearing of quantum interference discussed in a previous paper [S. Dürr, et al., Nature 395 (1998) 33] is explained in the same spirit as our recent papers [Ren De-Ming, Commun. Theor. Phys. (Beijing, China) 41 (2004) 685, 833].     

Quantum and quasiclassical dynamics of C(3P)+H2(1∑+g)→ H(2S)+CH(2Π)reaction:Coriolis coupling effects and stereodynamics

The dynamics of C+H2 → H+CH reaction is theoretically studied using the quasiclassical trajectory and quantum mechanical wave packet methods.The analysis of rea...