Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 015, 44 pages      arXiv:1110.3020      https://doi.org/10.3842/SIGMA.2012.015
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Learning about Quantum Gravity with a Couple of Nodes

Enrique F. Borja a, b, Iñaki Garay a, c and Francesca Vidotto d, e
a) Institute for Theoretical Physics III, University of Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
b) Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Facultad de Física, Universidad de Valencia, Burjassot-46100, Valencia, Spain
c) Departamento de Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
d) Laboratoire de Physique Subatomique et de Cosmologie, 53 rue des Martyrs, 38026 Grenoble, France
e) Centre de Physique Théorique de Luminy, Case 907, 13288 Marseille, France

Received October 08, 2011, in final form March 12, 2012; Published online March 25, 2012

Abstract
Loop Quantum Gravity provides a natural truncation of the infinite degrees of freedom of gravity, obtained by studying the theory on a given finite graph. We review this procedure and we present the construction of the canonical theory on a simple graph, formed by only two nodes. We review the U(N) framework, which provides a powerful tool for the canonical study of this model, and a formulation of the system based on spinors. We consider also the covariant theory, which permits to derive the model from a more complex formulation, paying special attention to the cosmological interpretation of the theory.

Key words: discrete gravity; canonical quantization; spinors; spinfoam; quantum cosmology.

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