Work

Lifting SU(2) spin networks to projected spin networks

Year: 2010

Type: article

Abstract: Projected spin network states are the canonical basis of quantum states of geometry for the recent EPRL-FK spinfoam models for quantum gravity introduced by Engle-Pereira-Rovelli-Livine and Freidel-Krasnov. They are functionals of both the Lorentz connection and the time-normal field. We analyze in detail the map from these projected spin networks to the standard SU(2) spin networks of loop quantum gravity. We show that this map is not one to one and that the corresponding ambiguity is parameterized by the Immirzi parameter. We conclude with a comparison of the scalar products between projected spin networks and SU(2) spin network states.

Source: Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

DOI: 10.1103/physrevd.82.064044

Authors: Maïté Dupuis, Etera R. Livine

Institutions: École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Laboratoire de Physique de l'ENS de Lyon

Language: English

Topic: Noncommutative and Quantum Gravity Theories

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2111008219

FWCI: 5.102

Cites: 32

Cited by: 79

Related to: 10