Racah Coefficients Of Basic Spinor Representations Of O(N) And Their Symmetries

Racah coefcients play essential roles in calculating energy levels and transitionrates of given physical systems, and in constructing the wavefunction of multi-particlesystems. On the other hand, Racah coefcients are basis-independent (i.e. independentof the projection quantum numbers). So Racah coefcients emerge as a very usefulmathematical tool.In this paper, we studied O(N) Racah coefcients of basic spinor representations.Firstly, we demonstrated the building-up process concerning calculating Racah coef-cients for the general Lie algebra G, by using those of sub-algebra H and G H reduc-tion factors. Then based on the known O(3) Racah coefcients and O(N) O(N1)reduction factors, we obtained analytic expressions for the O(N) Racah coefcients ofbasic spinor representations when N=4,5,6,7.These obtained results have many good regularities and several symmetries. Sym-metries considered here are classical symmetries,”mirror” symmetries, Regge sym-metries. We also fnd the similarities among the results of O(2n+1), which may beextended to all odd N.