圈量子引力中的基底变换

Basis Transformations in Loop Gravity

给出了自旋网表象中的两个4价基底,证明了它们之间的变换属酉变换。用重耦理论的图式计算法,推出了体积算符对基底作用的重耦矩阵的表式,并利用体积算符的本征值得到空间量子化的结果。

The two four--valent rescaled bases are obtained in the spin networks representation to prove that the change of the basis is a unitary transformation. Then the graph and the symbol expressions of the recoupling matrix used in action of volume operator on res- caled basis are obtained with the graph calculation method. Finally, the engenvalues of the volume operator and the space quantization are discussed.