Hamiltonian reduction of free particle motion on group SL(2, $\mathbb{R}$)

Abstract

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 $\mathrm{SL}(2,\mathbb{R})$ 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 $S^1\times \mathbb{R}$. Canonical coordinates are constructed for the both cases, and it is shown that in the first case the reduced phase space is symplectomorphic to the union of two cotangent bundles $T^{\ast }(\mathbb{R})$ endowed with the canonical symplectic structure, while in the second case it is symplectomorphic to the cotangent bundle $T^{\ast }(S^1)$ also endowed with the canonical symplectic structure.

12 pages, LaTeX file, to be publised in Teor. Mat. Fiz

References in corpus (2)

• Quantum mechanical Liouville model with attractive potential
• Regularization of Toda lattices by Hamiltonian reduction

Cited by in corpus (2)

• W-algebras for non-abelian Toda systems
• Geometric quantisation of the global Liouville mechanics