Stratified reduction of many-body dynamical systems. (English) Zbl 1318.70005

Iwai, Toshihiro

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 5–12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 149-157 (2004).

Summary: The center-of-mass system for many bodies in \(\mathbb R^3\) admits a natural action of the rotation group \(\mathrm{SO}(3)\). According to the orbit types for the \(\mathrm{SO}(3)\) 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.
For the entire collection see [Zbl 1048.53002].

MSC:

70F10	\(n\)-body problems
70H03	Lagrange’s equations
70H33	Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
81R05	Finite-dimensional groups and algebras motivated by physics and their representations