Coherent spin-networks

Journal Article · Thu Jul 15 04:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.82.024012· OSTI ID:21410122

Bianchi, Eugenio; Magliaro, Elena ^[1]; Perini, Claudio ^[1]

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1. Centre de Physique Theorique de Luminy, case 907, F-13288 Marseille (France)

In this paper we discuss a proposal of coherent states for loop quantum gravity. These states are labeled by a point in the phase space of general relativity as captured by a spin-network graph. They are defined as the gauge-invariant projection of a product over links of Hall's heat kernels for the cotangent bundle of SU(2). The labels of the state are written in terms of two unit vectors, a spin and an angle for each link of the graph. The heat-kernel time is chosen to be a function of the spin. These labels are the ones used in the spin-foam setting and admit a clear geometric interpretation. Moreover, the set of labels per link can be written as an element of SL(2,C). These states coincide with Thiemann's coherent states with the area operator as complexifier. We study the properties of semiclassicality of these states and show that, for large spins, they reproduce a superposition over spins of spin-networks with nodes labeled by Livine-Speziale coherent intertwiners. Moreover, the weight associated to spins on links turns out to be given by a Gaussian times a phase as originally proposed by Rovelli.

• OSTI ID: 21410122
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 82; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
ANNIHILATION OPERATORS
EIGENSTATES
ENERGY
FIELD THEORIES
GAUGE INVARIANCE
GENERAL RELATIVITY THEORY
HEAT
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
PARTICLE PROPERTIES
PHASE SPACE
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM OPERATORS
RELATIVITY THEORY
SIMULATION
SL GROUPS
SPACE
SPIN
SU GROUPS
SU-2 GROUPS
SYMMETRY GROUPS
WEIGHT