Liouville方程的八类精确解

利用Poisson括号的正则不变性求得了Liouville方程的八类精确解:1)“重力”势系统,2)谐振系统,3)正负平方幂函数势系统,4)双曲函数势系统,5)三角函数势系统,6)PschlTeller势系统,7)“引(斥)力”势系统和8)Kratzer势系统.得到了“化动量正则变换”的一般方法.在求解后两个系统Liouville方程的过程中还应用了Routh方法和Binet方法.关键词：     

超拟共形变换的Beltrami代数

本文构造了一种与超拟共形变换相联系的代数, 即超Beltrami代数.该代数包含两个超共形(N S R ) 代数作为子代数.关键词：     

c=3, N=2 超共形场论的Z2 Orbifold-Prime模型

讨论了二维环面上中心荷c=3, N=2 的超共形场论. 特别给出该理论的配分函数. 进一步,为了产生新的模型,回顾了一般的orbifold方法. 然后构造了模不变的Z2 Orbifold-Prime模型.     

c＝3，N＝2超共形场论的Z2 0rbifold—Prime模型

讨论了二维环面上中心荷c＝3，N＝2的超共形场论。特别给出该理论的配分函数，进一步，为了产生新的模型，回顾了一般的orbifold方法，然后构造了模不变的Z2 0rbifold—Prime模型。     

两维量子引力中的一种可解模型

通过标量物质场的引入研究了两维量子引力中波函数的可解性,并考虑了两维超引力模型中的类似问题.     

高维量子可积系统的精确解

量子多体问题或量子场论中有一类模型是可以精确求解的,这类模型称作量子可积模型.量子可积模型的主要特征是:系统的守恒量数目与系统自由度的数目相同(对于具有无限自由度的系统,守恒量的数目亦为无限),从而使系统的本征态、本征能谱及热力学量都可精确求得.自从1931年Bethe～[1]首次求得一维Heisenberg链的精确解后,许多一维量子多体物理模型或(1+1)维(一维空间加一维时间)量子场论模型都获得了精确解.这些精确解曾对于人们理解许多物理现象(如稀磁合金中的Kondo效应)起到了极为重要的作用.如何将这方面的理论推广到高维空间,即寻找并精…     

基于曲面基底偏振复用超表面的全息和隐身技术

共形超表面可以打破几何形状与光学功能之间的限制,可以显著改善任意曲面物体的光学特性,进而将超表面功能拓展到具有任意形状的组件中。当前尚未报道将偏振复用技术运用到共形超表面从而实现多偏振通道的多功能设计。文章设计了一种曲面基底的偏振复用超表面,基于传输相位调制原理设计了共形超表面的单元结构,使得超表面对不同偏振状态的入射光实现不同的相位调制,例如实现曲面全息和光学隐身等功能。这种共形超表面设计灵活性强,可以嵌入到各种非平面系统实现多功能,在军事安全、可穿戴电子设备等领域具有广泛应用前景。     

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。     

从可积条件到共形对称:玻色超共形Toda模型

本文研究从WZNW模型的二阶共形约化得到的新模型—玻色超共形Toda模型.从约化过程得出了模型的运动方程及Lax pair线性方程组,进而在主阶化的特殊情形下求出了r矩阵、基本Poisson关系.手征交换代数以及经典顶角算子.     

The Associative Algebras of Conformal Field Theory

Modulo the ideal generated by the derivative fields, the normal ordered product of holomorphic fields in two-dimensional conformal field theory yields a commutative and associative algebra. The zero mode algebra can be regarded as a deformation of the latter. Alternatively, it can be described as an associative quotient of the algebra given by a modified normal ordered product. We clarify the relation of these structures to Zhu's product and Zhu's algebra of the mathematical literature.     

Parafermion Fields Constructed by Current Algebra

In this letter, the parafermion fields constructed by current algebra are considered. It is proved that there must be a parafermion field with respect to each form of current algebra. We also obtain the corresponding representation and unitary relation of the parafermion field from any current algebra.     

Noninvariant zeta-function regularization in quantum Liouville theory

We consider two possible zeta-function regularization schemes of quantum Liouville theory. One refers to the Laplace–Beltrami operator covariant under conformal transformations, the other to the naive noninvariant operator. The first produces an invariant regularization which however does not give rise to a theory invariant under the full conformal group. The other is equivalent to the regularization proposed by A.B. Zamolodchikov and Al.B. Zamolodchikov and gives rise to a theory invariant under the full conformal group.     

The Nonchiral Fusion Rules in Rational Conformal Field Theories

We introduce a general method in order to construct the nonchiral fusion rules which determine the operator content of the operator product algebra for rational conformal field theories. We are particularly interested in the models of the complementary D-like solutions of the modular invariant partition functions with cyclic center Z_N. We find that the nonchiral fusion rules have a Z_N-grading structure.     

On Conformal Field Theory of SLE(κ,ρ)

SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-L?wner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = . The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(κ ρ)     

General Rotating Black Hole with Four Charges and Liouville Theory

By considering the dual Liouville theory emerging in the near-horizon limit, we study the thermodynamics of general rotating black hole with four charges in four dimensions. Both the black hole entropy and temperature are found to agree with the gravitational expectations. The relations between the new Liouville formalism and the anomaly approach are also discussed.     

Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k² (where k is a divisor of n) or 3k² if the spin of the simple current is half-integral and k is odd.Mathematical Subject Classifications (2000). 81T40.Work supported by grant OTKA TS044839.