Enrique F. Borja, Iñaki Garay, Francesca Vidotto, “Learning about quantum gravity with a couple of nodes”, SIGMA, 2012, Volume 8,015, 44 pp.

This article is cited in 17 papers

Learning about quantum gravity with a couple of nodes

Enrique F. Borja^ab, Iñaki Garay^ac, Francesca Vidotto^de

^a Institute for Theoretical Physics III, University of Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
^b Departamento de Física Teorica 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

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 $\mathrm{U}(N)$ 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.

Keywords: discrete gravity, canonical quantization, spinors, spinfoam, quantum cosmology.

MSC: 83C27; 83C45; 83C60; 83F05

Received: October 8, 2011; in final form March 12, 2012; Published online March 25, 2012

Language: English

DOI: 10.3842/SIGMA.2012.015