Quantization of Chern-Simons Theory à la Loop Quantum Gravity

Abstract

We consider the canonical loop quantization (following the loop quantum gravity (LQG) scheme) of Chern-Simons theory in a noncompact space with the topology of a cylinder. At quantum level, constraints are defined and completely solved, and we obtain a gauge and diffeomorphism invariant Hilbert space, which is infinite dimensional but separable. Some remarks about the inclusion of boundary are done.