Singular angular momentum mappings (Q1073413)

We algebraically reduce the system consisting of a nonrelativistic particle moving in \({\mathbb{R}}^ n\) with vanishing angular momentum J. After analyzing the conical structure of the constraint set \(J^{- 1}(0)\), we use algebraic geometric techniques to explicitly construct the reduced Poisson algebra of rotationally invariant observables. This procedure enables us to completely identify the effects of the singularity in \(J^{-1}(0)\) on the system. We then group-theoretically reduce the system and compare our results with those obtained algebraically.