体积算符对任意价顶角的本征作用与本征值谱

Eigenactions and eigenvalues of volume operator on any-valent vertices

利用体积算符所含抓三元组对自旋网任意价顶角中圈线作用的反称化和双元恒等式,证明了这种作用均为本征作用,本征值为-2.用代数方法给出了对任意价顶角求体积算符本征值的系统程式,得到了普遍情况下的3,4,5和6顶角体积本征值的具体代数表式.

Antisymmetrizing the actions of hand triple contained in volume operator and grasping on the segments rooting through anyvalent vortex of spin netwok, and using the binor identity, a proof is given that all these actions are eigenactions with eigenvalue -2. A systematic algebraic method to calculate the eigenvalues of volume operator for any-valent vortices is given, and the general and algebraic expressions of volume eigenvalues for 3-, 4-, 5-, 6- valent vertices are obtained.