Generalized boson algebras : their properties and applications to mathematics and physics

广义玻色子代数：它们的性质及其在数学和物理中的应用

基本信息

批准号：
15540132
负责人：
AIZAWA Naruhiko
金额：
$ 2.05万
依托单位：
Osaka Prefecture University (2005)Osaka Women's University (2003-2004)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

The purposes of this research project are three fold. Firstly, seeking possibilities of generalizing the boson algebra in the framework of Hopf algebra. Secondly, investigating properties of the generalized boson algebras. Then, applying the generalized boson algebras to some mathematical or physical problems. One of the generalized boson algebras, already known, is regarded as bosonization of the quantum algebra U_q[osp(1/2)]. We, thus, started our investigation with the algebra (denoted by U) and U_q[osp(1/2)]. The main results of the present research are summarized as follows.1.The algebra dual to U was obtained. The duality is expressed in the form of universal T-matrix.2.The single-particle and bipartite coherent states for U were constructed. It was shown that the bipartite coherent state had entanglement which disappears in the classical limit. An analytic proof of orthogonality and completeness for the single-particle coherent state was given.3.Irreducible representations of th … More e algebra dual to U were obtained explicitly and it was shown that the representation matrices are related to little q-Jacobi polynomials.4.Tensor product of the representations of U is decomposed into irreducible ones. It was shown that the decomposition was carried out with q-Hahn polynomials. The result No.3 and 4 imply that the algebra U gives a new algebraic background for basic hypergeometri functions.5.A general method for constructing noncommutative space with supersymmetric nature, which means that the space is covariant under the action of quantum group OSp_q(1/2), was introduced. By the method, 3-dimensional noncommutative flat superspace and 5-dimensional noncommutative supersphere were constructed and their properties, as well as relations to boson algebras, were studied.6.Differential geometry on noncommutative spaces has been developed by Dubois-Viollete et al. In this research, the geometry was extended to noncommutative superspaces. As an example, covariant derivative, curvature etc on 3-dimensional noncommutative superspace, which is a covariant algebra of the Jordanian quantum group OSp_h(1/2), were computed. The computation shows that the superspace is not physical, since the covariant derivative is not compatible with the metric. Less

该研究项目的目的是三倍。首先，寻求在霍普夫代数框架内概括玻色族代数的可能性。其次，研究广义玻色子代数的特性。然后，将广义的玻色子代数应用于一些数学或物理问题。已知的广义玻色子代数之一被认为是量子代数U_Q [OSP（1/2）]的玻殖化。因此，我们开始对代数（由U）和U_Q [OSP（1/2）]进行调查。本研究的主要结果总结如下。1。获得了u的代数双重。二元性以通用t矩阵的形式表示。结果表明，两部分相干状态具有纠缠，在经典极限内消失。给出了单粒子相干状态的正交性和完整性的分析证明。3.TH的可误差表示，您对U的d dual dual dual dual to t dual a dial complicial carliciental complicity cartical.4.temantiagations complications a表示条件与Q-Jacobi多项式很小有关。4。u decomptiations u decompentions u decomptiations u decompenting u decompents u decompents u decomposity。结果表明，分解是用Q-HAHN多项式进行的。第3和4号的结果表明，代数U给出了基本超切函数的新代数背景。5.一种用于构造具有超对称性质的非交通空间的通用方法，这意味着该空间在量子组OSP_Q（1/2）的作用下是协变量的。通过该方法，构建了三维非公平式扁平超空间和5维非交通性超球，其特性以及与波森代数的关系是研究。6。dubois-viollete et al and deffentiod.6。在这项研究中，几何形状扩展到非交通超级空间。例如，计算了3维非交通式超空间上的协变量，曲率等，这是约旦量子组OSP_H（1/2）的协变量代数。该计算表明超空间不是物理空间，因为协变量导数与度量不兼容。较少的