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arXiv · 0907.3240

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

Clisthenis P. Constantinidis·Gabriel Luchini·Olivier Piguet
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Abstract

As a laboratory for loop quantum gravity, we consider the canonical quantization of the three-dimensional Chern-Simons theory on a noncompact 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 completely solve them, thus constructing a gauge and diffeomorphism invariant physical Hilbert space for the theory. This space turns out to be infinite dimensional, but separable.

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Clisthenis P. Constantinidis, Gabriel Luchini, Olivier Piguet. 2010-03-02. The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach. https://doi.org/10.1088/0264-9381%2F27%2F6%2F065009

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