Coherent states for FLRW space-times in loop quantum gravity

Journal Article · Tue Feb 15 04:00:00 EST 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.044029· OSTI ID:21504992

Magliaro, Elena; Perini, Claudio ^[1]; Marciano, Antonino ^[2]

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1. Institute for Gravitation and the Cosmos, Physics Department, Penn State, University Park, Pennsylvania 16802-6300 (United States)
2. Department of Physics and Astronomy, Haverford College, Haverford, Pennsylvania 19041 (United States)

We construct a class of coherent spin-network states that capture properties of curved space-times of the Friedmann-Lamaitre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial (t=const) section with a dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex SL(2,C) variables, one for each link of the graph, and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in spin foams.

• OSTI ID: 21504992
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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