一般情况下二维非线性σ模型的等时Kac-Moody代数

在本文中对一般的紧致单纯群和耦合常数λ₀的任意值证明了带Wess-Zumino项的二维非线性σ模型的等时流代数构成带中心荷的Kac-Moody代数。 关键词：     

Chevalley基下WZNW场论的Hamilton形式

本文在半单Lie代数的Chevalley正则基下给出了二维WZNW场论的Hamilton形式,并在此基础上计算了守恒流之间的Poisson括号,结果正是经典的Kac-Moody流代数.     

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.     

引力场约化理论中的Virasoro代数

我们在引力场约化理论中找到了一种新的变换关系, 并且发现这种变换所对应的代数结构是没有中心项的Virasoro代数. 同Geroch群相比较, 不难确定在引力场约化理论中Virasoro代数与Kac-Moody代数之间的关系. 最后, 我们指出了这种变换可用来产生Ernst场方程的新解.     

(2+1)维破裂孤子方程的新多孤子解

Hirota双线性方法是一种非常有效的直接方法，使得求解非线性演化方程的多孤子解转化为 代数求解.将这一方法进一步拓展，求得了(2+1)维破裂孤子方程的新多孤子解. 关键词： 双线性方法 多孤子解 (2+1)维破裂孤子方程     

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■的整数阶化,我们研究了一大批共形约化WZNW模型的方案Cons[■(H,d)]。在正规约束的条件下,构造了W代数W[■(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。     

具有广义Virasoro对称代数的(3+1)维Painlevé可积模型

寻找高维可积模型(特别是3+1维可积模型)是非线性物理中的一个非常重要的问题.建立了一种利用广义Virasoro对称性的高维实现首先找到了一些(3+1)维Virasoro可积模型,并证明(3+1)维Virasoro可积模型均具有KacMoodyVirasoro对称代数.更进一步,利用WeissTaborCarnevale的奇性分析方法,证明了其中一个Virasoro可积模型也是Painlev啨可积的. 关键词： 广义Virasoro代数 Painlevé性质 (3+1)维可积模型     

互反型高维可积Kaup-Newell系统

可积系统研究是物理和数学等学科的重要研究课题.然而,通常的可积系统研究往往被限制在(1+1)维和(2+1)维,其原因是高维可积系统极其稀少.最近,我们发现利用形变术可以从低维可积系统导出大量的高维可积系统.本文利用形变术,将(1+1)维的Kaup-Newell(KN)系统推广到(4+1)维系统.新系统除了包含原来的(1+1)维的KN系统外,还包含三种(1+1)维KN系统的互反形式.模型也包含了许多新的(D+1)维(D≤3)的互反型可积系统.(4+1)维互反型KN系统的Lax可积性和对称可积性也被证明.新的互反型高维KN系统的求解非常困难.本文仅研究(2+1)维互反型导数非线性薛定谔方程的行波解,并给出薛定谔方程孤子解的隐函数表达式.     

(3+1)维非线性Burgers系统的新的分离变量解及其局域激发结构与分形结构

将扩展的Riccati方程映射法推广到了(3+1)维非线性Burgers系统，得到了系统的分离变量解；由于在解中含有一个关于自变量(x,y,z,t)的任意函数，通过对这个任意函数的适当选取，并借助于数学软件Mathematica进行数值模拟，得到了系统的新而丰富的局域激发结构和分形结构.结果表明，扩展的Riccati方程映射法在求解高维非线性系统时，仍然是一种行之有效的方法，并且可以得到比(2+1)维非线性系统更为丰富的局域激发结构. 关键词： 扩展的Riccati方程映射法 (3+1)维非线性Burgers方程 局域激发结构 分形结构     

O(N)超对称手征模型中的非定域无穷多守恒流与Kac-Moody代数结构

从Curtright-Zachos的O(N)超对称手征模型理论出发, 引入扩展的局域变换, 通过Noether分析得到了相应的非定域无穷多守恒流. 同时又证明了在这个理论中二维旋量场ψ的变分满足Kac-Moody类型代数关系.     

GROUP PROPERTY AND ALGEBRA STRUCTURE FOR A KIND OF BÄCKLUND TRANSFORMATIONS

We explain further the group property and algebra struc-tore for a kind of Bäcklund transformations. If the Lax repre- sentation of a given nonlinear (evolution) system is dependent on a complex spectral parameter fractional Zinearly, the Back-land transformations with respect to the principal pseudopoten- tials (fundamental solutions) of the Lax representation can be identified with solutions of the regular matrix Riemann-Hilbert problem. It is shown that this kind of Riemann-HIbert probl em constructs an infinite dimensional Lie group and its infinitesi- mal form presents itself the infinite dimensional algebra of Kac-Moody type.     

Extended non-abelian gauge symmetries in the classical WZNW model

Higher spin extensions of the non-Abelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. It is a characteristic property of the WZNW model that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases, the higher spin Noether currents do not span an invariant space with respect to their generating transformations. Here, the current space is extended to an invariant space which allows us to gauge the symmetry.Supported by Bulgarian Foundation on Fundamental Research under contract Ph-318/93-95.     

Algebraic properties of the 1 + 1-dimensional Heisenberg spin field model

The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete prolongation Lie algebra, a whole family of nonlinear field equations containing the original Heisenberg system is generated.     

Hidden quantum groups inside Kac-Moody algebra

A lattice analogue of the Kac-Moody algebra is constructed. It is shown that the generators of the quantum algebra with the deformation parameterq=exp(iπ/k+h) can be constructed in terms of generators of the lattice Kac-Moody algebra (LKM) with the central chargek. It appears that there exists a natural correspondence between representations of the LKM algebra and the finite dimensional quantum group. The tensor product for representations of the LKM algebra and the finite dimensional quantum algebra is suggested.     

Non-linear realization of the virasoro-Kac-Moody algebra and the anomalies

The non-linear realization of the Virasoro algebra ⊛ Kac-Moody algebra will be studied. We will calculate the Ricci tensor of the relevant Kähler manifold to show a new vacuum structure for this coupled algebra.     

一般情况下二维非线性_模型的等时Kac-Moody代数

在本文中对一般的紧致单纯群和祸合常数 的任意值证明了带Wess-Zumino 项的二维非线性a 模型的等时流代数构成带中心荷的Kac-Mody 代数. 关键词：     

KAC-MOODY ALGEBRA FOR TWO DIMENSIONAL PRINCIPAL CHIRPL MODELS

A Darbou transformation depending on single continuous parameter t is constructed for a principal chiral field. The transformation forms a nonlinear representation of the group for any fixed value of t. Part of the kernel in the Riemann- Hilbert transform is shown to be-related to the Darboux trans- formation with its generators forming a Kac-Moody algebra. Conserved currents associated with the Kac-Moody algebra of the linearized equations and the Noether current for the group transformations with fixed value of t are obtained.     

ON THE TWO DIMENSIONAL NON-LINEAR σ MODEL WITH WESS-ZUMINO TERM II QUANTUM THEORY

The canonical quantization is carried out for the two dimensional non-Linear a model with wess-2umino term. It is shown that the currents in this model satisfy a Kac-Moody algebra for arbitrary values of the coupling constant.