Colloquium

Classical and Quantum Dynamics for an Extended Free Rigid Body

多羅間 大輔

1月23日(金) 13時30分

We define the classical and quantum dynamics for an extended free rigid body of dimension three and analyse them. The inverse of the inertia tensors, which are positive-definite symmetric matrices in the ordinary case, are extended to arbitrary symmetric ones. The classical dynamics can be analysed from the viewpoint of certain Lie-Poisson structures on the Euclidean space of dimension three. We also analyse the dynamics on the energy surfaces, fixed points on the energy surfaces, and their stability. The quantum dynamics are formulated as the problem of the simultaneous spectral resolution of the two operators over some Lie groups which correspond to the first integrals of the classical dynamics. We deal this problem with the Plancherel formula and we can get the explicit spectral resolution when the rigid body concerned is a symmetric top.