Model spaces as constrained Hamiltonian systems

Three dimensional gravity in Fefferman-Graham or BMS gauge is entirely described by the coadjoint representation of its asymptotic asymptotic symmetry group. A group-theoretical attempt at quantization requires one to quantize not only individual but the whole collection of coadjoint orbits. This is where model spaces come in. We propose a definition of a model space for generic Lie groups in terms of constrained Hamiltonian systems and begin by studying its quantization in the simplest case of SU(2).

 

Based on work in preparation done in collaboration with Thomas Smoes