Reduced SL(2,R) WZNW Quantum Mechanics

Abstract

The $SL(2,\mathbb{R})$ WZNW $\to$ Liouville reduction leads to a nontrivial phase space on the classical level both in $0+1$ and $1+1$ dimensions. To study the consequences in the quantum theory, the quantum mechanics of the $0+1$ dimensional, point particle version of the constrained WZNW model is investigated. The spectrum and the eigenfunctions of the obtained---rather nontrivial---theory are given, and the physical connection between the pieces of the reduced configuration space is discussed in all the possible cases of the constraint parameters.

LaTeX file, 33 pages. Results extended, contains all technical information not detailed in version to appear in J. Math. Phys

References in corpus (2)

• Global Aspects of the WZNW Reduction to Toda Theories
• Quantization of a relativistic particle on the SL(2,R) manifold based on Hamiltonian reduction

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