圈量子引力中作用于重标基的重耦矩阵

数学物理学报

圈量子引力中作用于重标基的重耦矩阵

¹邵丹;²邵亮; ³邵常贵; ³肖明

(1.江汉大学光电信息研究所武汉 430056; 2.武汉科技大学理学院应用物理系武汉430081; 3.湖北第二师范学院理论物理研究所武汉 430205)

收稿日期:2006-05-17 修回日期:2008-04-28 出版日期:2009-02-25 发布日期:2009-02-25
通讯作者: 邵丹
基金资助:
湖北省自然科学基金青年杰出人才项目（2007ABB031）和教育部留学回国人员科研启动基金（教外司留24号）资助.

Recoupling Matrix of Action on Rescaled Basis in Loop Gravity

¹Shao Dan; ²Shao Liang; ³Shao Changgui; ³Xiao Ming

(1.Institute of Light and Electronic Information, Jianghan University, Wuhan 430056; 2.Applied Physics Department, Wuhan University of Science and Technology, Wuhan 430081; 3.Institute of Theoretical Physics, Hubei University of Education, Wuhan 430205)

Received:2006-05-17 Revised:2008-04-28 Online:2009-02-25 Published:2009-02-25
Contact: Shao Dan

摘要/Abstract

摘要： 通过由重耦定理联系着的4价顶角进行基底改变, 给出了自旋结网圈表象中的两个4价重标基,
证明了它们之间的变换属于酉变换. 用重耦理论的图式计算法, 推出了体积算符对重标基作用可
直接计算的重耦矩阵的图形表式和记号表式, 并利用体积算符的本征值得到空间量子化的结果.

关键词: 自旋结网表象, 体积算符, 基底改变, 重耦矩阵.

Abstract: Using the basis change for four-valent vertices which are connected with the recoupling theorem two four-valent rescaled bases are obtained in the spin networks representation, and it is proved that the basis change is a unitary transformation. The graph and the symbol expressions of the recoupling matrix used in action of volume operator on rescaled basis are obtained with the graph calculation method. Finally the eigenvalues of the volume operator and the space quantization are discussed.

Key words: Spin networks representation, Volume operator, Basis change, Recoupling matrix.

中图分类号:

83B14

邵丹; 邵亮; 邵常贵; 肖明. 圈量子引力中作用于重标基的重耦矩阵[J]. 数学物理学报, 2009, 29(1): 158-164.

Shao Dan; Shao Liang; Shao Changgui; Xiao Ming. Recoupling Matrix of Action on Rescaled Basis in Loop Gravity[J]. Acta mathematica scientia,Series A, 2009, 29(1): 158-164.