圈量子引力中作用于重标基的重耦矩阵

Recoupling Matrix of Action on Rescaled Basis in Loop Gravity

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.

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.