Rosen-MorseⅡ势函数的Klein-Gordon方程和Dirac方程束缚态的精确解

在标量势和矢量势相等的情形, 研究了Rosen-MorseⅡ势的相对论效应, 应用超对称和形状不变势方法通过求解Klein-Gordon方程和Dirac方程得到了束缚态能量本征值, 最后, 讨论了Rosen-MorseⅡ势的一种特殊情况.     

不变本征算符法计算各向异性海森伯亚铁磁系统的自旋波能量

利用不变本征算符法计算了X-Y-Z模型各向异性海森伯亚铁磁系统的自旋波能量,并讨论了此系统特殊情形下的自旋波能量及不变本征算符法的优点与不足.     

具有广义Kratzer势的三维薛定谔方程的精确解

用超对称量子力学方法讨论了广义Kratzer势的形状不变性,并计算了它的能量本征值.传统的Kratzer势和改进的Kratzer势都是广义Kratzer势的特例.在此基础上,计算了双原子分子CO和NO在不同的径向量子数n_r和角量子数l时的能量本征值的具体数值.     

Dirac类氢原子的超对称方法研究

应用超对称方法研究了Ｄｉｒａｃ类氢原子问题，不需繁琐的数学处理，得到和严格解法完全一致的能量本征值谱及相应的本征函数。     

用超对称幺正变换解双光子过程的Jaynes-Cummings模型

本文发现了描写双光子过程的Jaynes-Cummings哈密顿量的超对称结构.根据超对称量子力学理论,引入了超对称幺正变换使其哈密顿量对角化.从而,得到了它的本征值、本征态,同时也计算了态的演化和跃迁几率.     

在FBF背景下带反射边界条件的超对称t-J模型的代数Bethe ansatz方法

在阶化量子反散射的框架中,得到FBF背景下,带反射边界条件的超对称t－J模型的本征值和本征矢,及相应的Betheansatz方程．     

在FBF背景下带反射边界条件的超对称t–J模型的代数Bethe ansatz方法

在阶化量子反散射的框架中,得到FBF背景下,带反射边界条件的超对称t–J模型的本征值和本征矢,及相应的Betheansatz方程.     

非线性超场和夸克禁闭

利用非线性超场技术,我们讨论了超对称的非线性场论模型.找到了超对称运动方程精确静态解的一般形式,它可以作为袋模型的出发点。作为一个特殊情形,我们重新得到了 SLAC 袋模型,也就是说,SLAC 袋是超对称的.文中还讨论了超对称的 Sine-Gordon 模型、Sinh 模型和 exp 模型.     

用超对称幺正变换解扩展的J—C模型

研究发现对于描述强度有关的辐射场与二能级原子的相互作用的J－C哈密吨量存在超对称结构,用超对称幺正变换将哈密顿量对角化,得到了它的本征方程和本征值。     

Hulthen势场中Schrdinger方程束缚态问题的超对称量子力学

应用超对称量子力学 (SQM)方法得到了具有Hulthen势的Schr dinger方程能量本征值谱和本征函数的精确解 .分析表明 :Hulthen势是一种形状不变势 ,Hulthen势场中量子力学束缚态的数目是有限的 .     

Integrable extensions of N = 2 supersymmetric KdV hierarchy associated with the nonuniqueness of the roots of the Lax operator

We present new supersymmetric integrable extensions of the a = 4, N = 2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generates a new hierarchy of integrable equations, for which we investigate the Hamiltonian structure. In a special case our system describes the interaction of the KdV equation with the two MKdV equations.     

The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model

Calculations of the ultraviolet counterterms of the bosonic and supersymmetric nonlinear σ-models in two space-time dimensions are undertaken in order to verify conclusions of a recent argument based on differential geometry in the supersymmetric case. The background field method and the normal coordinate expansion are discussed in detail, and the generalized renormalization group pole equations applicable to the nonlinear σ-model are derived. Both component and superfield calculations of the counterterms are presented.     

No‐go result for supersymmetric gauge theories in the causal approach

We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non‐Abelian gauge theory (SUSY‐QCD) is uniquely determined by some natural assumptions, as in the case of Yang‐Mills models. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.     

Higher-Order Inhomogeneous Generalized Heisenberg Supermagnetic Model

We construct the fourth-order inhomogeneous generalized HS model and investigate the integrability property of the supersymmetric integrable system. Moreover, in terms of the gauge transformation, we investigate the corresponding gauge equivalent counterparts under two constraints, i.e., the super inhomogeneous generalized nonlinear Schr?dinger equation and the fermionic inhomogeneous generalized nonlinear Schr?dinger equation.     

Jaynes-Cummings Hamiltonian Describing an Atomic Four-level Double Λ Configuration Diagonalized by Virtue of Supersymmetric Transformation

By introducing the four-level state ket-bra operators as atomic variables, we show that the Hamiltonian of a four-level system with two lower levels and two top levels, which are respectively almost degenerate, interacting with four light fields through double Λ configuration process, can be reformed as a standard Jaynes-Cummings Hamiltonian. Then the supersymmetric transformation method can be employed to diagonalize the Hamiltonian. This approach may be generalized to tackle other atom-photon interaction models since the supersymmetric transformation method is concise.     

N = 4 supersymmetric quantum mechanics and its large order behaviour

A model of N = 4 supersymmetric quantum mechanics is shown to have a perturbative expansion for which the large order behaviour is - (3/2)ⁿn!(9/π + 5/n + …). In the space of the coupling constants the supersymmetric case is found to be the dividing point between two different types of large order behaviour. In this way the large order behaviour of supersymmetric theories is special.     

The N = 2 supersymmetric Toda lattice hierarchy

We propose a new integrable N = 2 supersymmetric Toda lattice hierarchy which may be relevant for constructing a supersymmetric one-matrix model. We define its first two Hamiltonian structures, the recursion operator and Lax-pair representation. We provide partial evidence for the existence of an infinite-dimensional N = 2 superalgebra of its flows. We study its bosonic limit and introduce new Lax-pair representations for the bosonic Toda lattice hierarchy. Finally we discuss the relevance this approach for constructing N = 2 supersymmetric generalized Toda lattice hierarchies.     

Generalized Kähler Geometry from Supersymmetric Sigma Models

We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri (Generalized complex geometry, DPhil thesis, Oxford University, 2004) regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of Gates et al. (Nucl Phys B248:157, 1984). When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.     

Revisiting novel symmetries in coupled ${ \mathcal N }=2$ supersymmetric quantum systems: examples and supervariable approach

We revisit the novel symmetries in ${ \mathcal N }=2$ supersymmetric quantum mechanical models by considering specific examples of coupled systems. Further, we extend our analysis to a general case and list out all the novel symmetries. In each case, we show the existence of two sets of discrete symmetries that correspond to the Hodge duality operator of differential geometry. Thus, we are able to provide a proof of the conjecture which points out the existence of more than one set of discrete symmetry transformations corresponding to the Hodge duality operator. Moreover, we derive on-shell nilpotent symmetries for a generalized superpotential within the framework of supervariable approach.     

Higgs bundles and four manifolds

It is known that the Seiberg–Witten invariants, derived from supersymmetric Yang–Mill theories in four dimensions, do not distinguish smooth structure of certain non-simply-connected four manifolds. We propose generalizations of Donaldson–Witten and Vafa–Witten theories on a Kähler manifold based on Higgs bundles. We showed, in particular, that the partition function of our generalized Vafa–Witten theory can be written as the sum of contributions our generalized Donaldson–Witten invariants and generalized Seiberg–Witten invariants. The resulting generalized Seiberg–Witten invariants might have, conjecturally, information on smooth structure beyond the original Seiberg–Witten invariants for non-simply-connected case.