Stratified Reduction of Many-Body Dynamical Systems

Abstract

The center-of-mass system for many bodies in $\mathbb{R}^3$ admits a natural action of the rotation group $SO(3)$. According to the orbit types for the $SO(3)$ action, the center-of-mass system $M$ is stratified into strata. A quantum Hamiltonian system and a classical Lagrangian system are defined on $L^2(M)$ and on $T(M)$, respectively. These systems are also stratified according to the stratification of $M$, and then reduced by the rotational symmetry, respectively.