Abstract
Here 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. (author). 8 refs.
Mladenov, I M;
[1]
Tsanov, V V
[2]
- International Centre for Theoretical Physics, Trieste (Italy)
- Sofia Univ., Sofia (Bulgaria). Dept. of Mathematics
Citation Formats
Mladenov, I M, and Tsanov, V V.
Geometric quantization of the momentum mapping associated with coupled harmonic oscillators.
IAEA: N. p.,
1991.
Web.
Mladenov, I M, & Tsanov, V V.
Geometric quantization of the momentum mapping associated with coupled harmonic oscillators.
IAEA.
Mladenov, I M, and Tsanov, V V.
1991.
"Geometric quantization of the momentum mapping associated with coupled harmonic oscillators."
IAEA.
@misc{etde_10132850,
title = {Geometric quantization of the momentum mapping associated with coupled harmonic oscillators}
author = {Mladenov, I M, and Tsanov, V V}
abstractNote = {Here 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. (author). 8 refs.}
place = {IAEA}
year = {1991}
month = {May}
}
title = {Geometric quantization of the momentum mapping associated with coupled harmonic oscillators}
author = {Mladenov, I M, and Tsanov, V V}
abstractNote = {Here 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. (author). 8 refs.}
place = {IAEA}
year = {1991}
month = {May}
}