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IHEP 96 - 40
(in Russian) | |
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| A.V. Razumov A.V., V.I. Yasnov | ||
| Hamiltonian Reduction of Free Particle Motion on Group SL(2,R) | ||
| Protvino, 1996.- p.13, refs.:6. | ||
The structure of the reduced phase space arising in the hamiltonian reduction of the phase space corresponding to a free particle motion on the group ${\rm SL}(2, {\Bbb R})$ is investigated. The considered reduction is based on the constraints similar to those used in the hamiltonian reduction of the Wess--Zumino--Novikov--Witten model to Toda systems. It is shown that the reduced phase space is diffeomorphic either to the union of two two--dimensional planes, or to the cylinder $S^1 \times {\Bbb R}$. Canonical coordinates are constructed for the both cases, and it is shown that in the first case the reduced phase space is sympectomorphic to the union of two cotangent bundles $T^*({\Bbb R})$ endowed with the canonical symplectic structure, while in the second case it is symplectomorphic to the cotangent bundle $T^*(S^1)$ also endowed with the canonical sympectic structure.
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