1304.1474 (Rodolfo Gambini et al.)

The SL(2,R) totally constrained model: three quantization approaches    [PDF]

Rodolfo Gambini, Javier Olmedo

We provide a detailed comparison of the different approaches available for the quantization of a totally constrained system whose constraint algebra corresponds to a non-compact $SL(2,\mathbb{R})$ Lie algebra. In particular, we consider three schemes: the Refined Algebraic Quantization, the Master Constraint Programme and the Uniform Discretizations approach. For the latter, we provide a quantum description where the physical Hilbert space is a subspace of the kinematical one whose basic bricks are eigenstates of the Hamiltonian associated to the infrarred counterpart of its discrete spectrum. We conclude that our physical Hilbert space together with a (quantum-mechanically) modified $so(2,1)\times so(2,1)$ observable algebra reproduces a semiclassical limit compatible with the continuum theory, up to corrections of the Planck order.

View original: http://arxiv.org/abs/1304.1474