Reduction of quantum systems with symmetry, continuous and discrete

岩井 敏洋


Reduction of dynamical systems is closely related with symmetry. The purpose of this talk is to show that Fourier analysis both on compact Lie groups and on finite groups serve as reduction procedure for quantum systems on an equal footing. The reduction procedure is applied to systems of many identical particles lying in ${\bf R}^3$ which admit the action of a rotation group $SO(3)$ and of a symmetric group or a permutation group.