## Abstract

The state space of Loop Quantum Gravity admits a decomposition into orthogonal subspaces associated to diffeomorphism equivalence classes of spin-network graphs. In this paper I investigate the possibility of obtaining this state space from the quantization of a topological field theory with many degrees of freedom. The starting point is a 3-manifold with a network of defect-lines. A locally-flat connection on this manifold can have non-trivial holonomy around non-contractible loops. This is in fact the mathematical origin of the Aharonov-Bohm effect. I quantize this theory using standard field theoretical methods. The functional integral defining the scalar product is shown to reduce to a finite dimensional integral over moduli space. A non-trivial measure given by the Faddeev-Popov determinant is derived. I argue that the scalar product obtained coincides with the one used in Loop Quantum Gravity. I provide an explicit derivation in the case of a single defect-line, corresponding to a single loop in Loop Quantum Gravity. Moreover, I discuss the relation with spin-networks as used in the context of spin foam models.

Original language | English (US) |
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Article number | 1668 |

Pages (from-to) | 1-23 |

Number of pages | 23 |

Journal | General Relativity and Gravitation |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2014 |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy (miscellaneous)