The Hilbert space of Chern-Simons theory on the cylinder. A Loop Qantum Gravity approach

Abstract

We consider the canonical quantization of three-dimensional Chern-Simons theory on a space with the topology of a cylinder. Working within the loop quantization formalism, we define at the quantum level the constraints appearing in the canonical approach and solve them, thus constructing the gauge and diffeomorphism invariant physical Hilbert space of the theory. This space is infinite dimensional, but separable.

Cite this paper

@inproceedings{Constantinidis2009TheHS, title={The Hilbert space of Chern-Simons theory on the cylinder. A Loop Qantum Gravity approach}, author={Clisthenis P. Constantinidis and Gabriel Luchini and Olivier Piguet}, year={2009} }