Learning about Quantum Gravity with a Couple of Nodes

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• Main Authors: Borja, E.F., Garay, I., Vidotto, F.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148405
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Learning about Quantum Gravity with a Couple of Nodes / E.F. Borja, I. Garay, F. Vidotto // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 109 назв. — англ.

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.