osp（1│4）Toda模型解的构造

将Ｌｅｚｎｏｖ－Ｓａｖｅｌｉｅｖ代数分析和Ｄｒｉｎｆｅｌｄ－Ｓｏｋｏｌｏｖ构造这种方法地称情形,并运用这种方法给出ｏｓｐ（１│４）Ｔｏｄａ模型的解,从而将这种方法推广到二秩情况。     

Legendre's relation and the quantum equivalence osp(4|4)1 = osp(2|2)−2 ⊕ su(2)0

Using explicit results for the four-point correlation functions of the Wess–Zumino–Novikov–Witten (WZNW) model we discuss the conformal embedding osp(4|4)₁ = osp(2|2)₋₂ ⊕ su(2)₀. This embedding has emerged in Bernard and LeClair's recent paper cond-mat/003075. Given that the osp(4|4)₁ WZNW model is a free theory with power law correlation functions, whereas the su(2)₀ and osp(2|2)₋₂ models are CFTs with logarithmic correlation functions, one immediately wonders whether or not it is possible to combine these logarithms and obtain simple power laws. Indeed, this very concern has been raised in a revised version of cond-mat/003075. In this paper we demonstrate how one may recover the free field behaviour from a braiding of the solutions of the su(2)₀ and osp(2|2)₋₂ Knizhnik–Zamolodchikov equations. We do this by implementing a procedure analogous to the conformal bootstrap programme Nucl. Phys. B 241 (1984) 333. Our ability to recover such simple behaviour relies on a remarkable identity in the theory of elliptic integrals known as Legendre's relation.     

经典李代数Dr上推广的Toda力学系统

根据经典李代数D_r根系的特点构造Laxpair,得到李代数D_r上推广的Toda链(这些链用一组有序整数(m,n)表示,m、n分别表示正、负根的级数),并给出m,n≤3时系统的运动方程、哈密顿量以及泊松括号的具体形式.     

满足互补原理的SO(10)×SU(4)手征前子模型

本文反MAC (Most Attractive Channel)规则推广到半单超色规范群情形,构造了满足互补原理的SO(10)×SU(4)手征前子模型.该模型给出唯一解,预言了4代夸克和轻子,没有例外粒子出现.本文引入了代规范群SU(2)_g讨论了不同代费米子质量简并性的破缺.     

WZNW模型的共形约化,扩展的手征代数及相应的Toda类可积模型(Ⅰ)一般构架

利用李代数g的整数阶化,我们研究了一大批共形约化WZNW模型的方案Cons[g(H,d)].在正规约束的条件下,构造了W代数W[g(H,d)]的基——约束Kac-Moody流的O'Raifeartaigh规范,并导出了相应于每个W代数的广义Toda类可积模型的运动方程.     

(2+1)维手征Gross-Neveu模型的Ward-Takahashi恒等式和质量谱

本文利用含复合场的手征Ward-Takahashi恒等式讨论了(2+1)维手征Gross-Neveu模型的费米子质量和束缚态的谱性质.在最低阶近似下,质量谱与大N展开的结果一致.当手征对称是一种近似的对称性时,得到了轴矢流部分守恒.     

(2+1)维手征Gross-Neveu模型的顶角修正和相结构

本文在1/N展开下计算了(2+1)维手征Gross-Neveu模型的顶角修正和费米子质量修正,并根据手征Ward-Takahashi恒等式得到的费米子质量公式讨论了1/N阶的相结构.结果表明,利用手征Ward-Takahashi恒等式来研究手征对称性的破缺有利于讨论手征对称性的高阶性质.     

超Liouville模型精确解

运用Leznov-Saveliev代数分析方法和Drinfeld-Sokolov构造分别给出超协变形式和分量形式超Liouville模型精确解.     

由3个不同的初始手征角给出的初次迭代后的自洽手征孤子解 (英文)

利用3 个不同的初始手征角,给出了重子数为1 的体系的平均场方程的一次迭代后的解,以此研究哪一种手征角可以令平均场方程的解的自洽性更快地达到。对于不同的初始手征角,发现经过第一次迭代后,指数形式的手征角给出的结果比别的手征角更接近自洽解的形状。We use three different initial chiral angle to give the solution of the mean-field equation of the system with baryon number B = 1 for the first iteration, to investigate which initial chiral angle will make the self-consistency reach faster. From the first iteration from different initial chiral angle, we found that the result from the inverse trigonometric form chiral angle is closer to the self-consistent one than the other two initial chiral angles.     

量子(超)代数在qp=1时的循环表示

利用商模方法和q-boson实现方法研究了量子(超)代数在q^p=1时的循环表示.对于与任意有限维单李代数相关的量子代数给出了两种方法的一般理论,而且推广到了量子超代数U_qosp(1.2).通过构造q-Heisenberg-Wey1超代数的循环表示,q-boson实现方法推广到构造某些高秩量子超代数的循环表示.     

The Solution Construction of Heterotic Super-Liouville Model

We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liou ville model, we obtain the conserved current and conserved charge which possessed the BR ST properties.     

The Solution Construction of Heterotic Super-Liouville Model

We investigate the heterotic super-Liouville model on the base of the basic Lie super-algebra Osp(1|2).Using the super extension of Leznov-Saveliev analysis and Drinfeld Sokolov linear system, we construct the explicit solution of the heterotic super-Liouville system in component form. We also show that the solutions are local and periodic by calculating the exchange relation of the solution. Finally starting from the action of heterotic super-Liou ville model, we obtain the conserved current and conserved charge which possessed the BR ST properties.     

Drinfeld-Sokolov Construction of Heterotic Toda Model

A free field representation for the left-right asymmetric conformal Toda theory based on simplf-laced even-rank Lie algebras is given. It is shown that the classical chiral exchange algebra for such theories can be reconstructed from free chiral bosons via Drinfeld-Sokolov linear systems, and is a bit more complicated than that of the standard Toda due to some additional δ-function terms and extra degrees of freedom.     

Bethe Vectors of the osp(1|2) Gaudin Model

The eigenvectors of the osp(1|2) invariant Gaudin Hamiltonians are found using explicitly constructed creation operators. Commutation relations between the creation operators and the generators of the loop superalgebra are calculated. The coordinate representation of the Bethe states is presented. The relation between the Bethe vectors and solutions to the Knizhnik–Zamolodchikov equation yields the norm of the eigenvectors.     

sl(1|2) Super-Toda Fields

Explicit exact solution of supersymmetric Toda fields associated with the Lie superalgebra sl(2|1) is constructed. The approach used is a super extension of Leznov-Saveliev algebraic analysis, which is based on a pair of chiral and antichiral Drienfeld-Sokolov systems. Though such approach is well understood for Toda field theories associated with ordinary Lie algebras, its super analogue was only successful in the super Liouville case with the underlying Lie superalgebra osp(1|2). The problem lies in that a key step in the construction makes use of the tensor product decomposition of the highest weight representations of the underlying Lie superalgebra, which is not clear until recently. So our construction made in this paper presents a first explicit example of Leznov-Saveliev analysis for super Toda systems associated with underlying Lie superalgebras of the rank higher than 1.     

Universal R-matrix of the quantum superalgebra osp(2 | 1)

A quantum analogue of the simplest superalgebra osp(2 | 1) and its finite-dimensional, irreducible representations are found. The corresponding constant solution to the Yang-Baxter equation is constructed and is used to formulate the Hopf superalgebra of functions on the quantum supergroup OSp(2 | 1).     

On Two-Parameter Deformations of osp(1|2)(1)

An elliptic two-parameter deformation of the (universal enveloping superalgebra of) affine Lie superalgebra osp(1|2)⁽¹⁾ is proposed in terms of free boson realization. This deformed superalgebra is shown to fit in the framework of infinite Hopf family of superalgebras, a generalization of the infinite Hopf family of algebras proposed earlier by the authors. The trigonometric and rational degenerations are briefly discussed.     

Solution of the Semi-Infinite Toda Lattice for Unbounded Sequences

The semi-infinite Toda lattice is the system of differential equations d _n (t)/dt = _n (t)(b _n+1(t) – b _n (t)), db _n (t)/dt = 2( _n ²(t) – _n–1 ²(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences _n (t), b _n (t) which satisfy the conditions _n (0) = _n ,, b _n (0) = b _n , where _n > 0 and b _n are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences _n and b _n are bounded. When at least one of the known sequences _n and b _n is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences _n and b _n such that the system has a unique solution. The results are illustrated with a typical example where the sequences _i (t), b _i (t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d²/dt ² log h _n = h _n+1 + h _n–1 – 2h _n , n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation.