Geometric quantization of the momentum mapping associated with coupled harmonic oscillators
Abstract
We study a mechanical system whose dynamics is governed by a pair of commuting Hamiltonians which can be considered as the components of the momentum mapping associated with a torus action. We reduce the system via this momentum map and apply the geometric quantization scheme to its orbit manifold. In this way we obtain the energy levels along with the corresponding multiplicities. Finally, we point out that our considerations can be easily generalized giving in this way a new insight into the theory of representations of Lie groups in terms of Hamiltonian Mechanics.
 Publication:

Unknown
 Pub Date:
 May 1991
 Bibcode:
 1991gqmm.rept.....M
 Keywords:

 Field Theory (Physics);
 Hamiltonian Functions;
 Harmonic Oscillators;
 Lie Groups;
 Momentum;
 Momentum Theory;
 Quantum Mechanics;
 Quantum Theory;
 Classical Mechanics;
 Energy Levels;
 Manifolds (Mathematics);
 Toruses;
 Thermodynamics and Statistical Physics