Lifting SU(2) spin networks to projected spin networks

Journal Article · Wed Sep 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.064044· OSTI ID:21421184

Dupuis, Maiete; Livine, Etera R ^[1]

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1. Laboratoire de Physique, ENS Lyon, CNRS-UMR 5672, 46 Allee d'Italie, Lyon 69007 (France)

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.

• OSTI ID: 21421184
• Journal Information: Physical Review. D, Particles Fields, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevD.82.064044; (c) 2010 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPARATIVE EVALUATIONS
FUNCTIONALS
QUANTUM GRAVITY
SPIN
SU-2 GROUPS
ANGULAR MOMENTUM
EVALUATION
FIELD THEORIES
FUNCTIONS
LIE GROUPS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
SU GROUPS
SYMMETRY GROUPS