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Advances in Mathematical Physics
Volume 2015, Article ID 307132, 8 pages
Research Article

Loop Quantization of a 3D Abelian BF Model with σ-Model Matter

1Departamento de Física, Universidade Federal do Espírito Santo (UFES), 29075-910 Vitória, ES, Brazil
2Departamento de Física, Universidade Federal de Viçosa (UFV), 36570-900 Viçosa, MG, Brazil

Received 10 November 2014; Revised 18 December 2014; Accepted 19 December 2014

Academic Editor: Shao-Ming Fei

Copyright © 2015 Diego C. M. Mendonça and Olivier Piguet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The main goal of this work is to explore the symmetries and develop the dynamics associated with a 3D Abelian BF model coupled to scalar fields submitted to a sigma model like constraint, at the classical and quantum levels. Background independence, on which the model is founded, strongly constrains its nature. We adapt to the present model the techniques of Loop Quantum Gravity in order to construct its physical Hilbert space and its observables.