Classical and quantum mechanics of a pseudo-rigid body in three dimensions

This paper is a continuation of a previous one (Iwai 2010 J. Phys. A: Math. Theor. 43 095206), in which the geometry and mechanics of the pseudo-rigid body in n dimensions are studied. Though the dimension is restricted to n = 3 in this paper, the quantization of the pseudo-rigid body is performed. Further, a detailed study is carried out for the reduction of the pseudo-rigid body by the SO(3) x SO(3) symmetry and thereby the boundary behavior of the kinetic energy is investigated. It is shown that both in classical and quantum mechanics, the reduced Hamiltonian, which looks singular at the boundary of the base space, takes finite values on the boundary. In addition, reduction is performed not only by symmetry but also by averaging 'fast' variables, and thereby an averaged force comes out, which can be viewed as an entropic force.