Łukasz Szulc 2007 Class. Quantum Grav. 24 6191 doi:10.1088/0264-9381/24/24/003
Łukasz Szulc
Show affiliationsAn open FRW model in loop quantum cosmology is considered. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of k = −1 it is possible to construct a suitable loop which provides us with the quantum scalar constraint originally introduced by Vandersloot [19]. The quantum scalar constraint operator with negative cosmological constant is proved to be essentially self-adjoint.
85A40 Cosmology (For relativistic cosmology, see 83F05)
83C45 Quantization of the gravitational field
57R25 Vector fields, frame fields
51M10 Hyperbolic and elliptic geometries (general) and generalizations
Issue 24 (21 December 2007)
Received 13 July 2007, in final form 29 October 2007
Published 27 November 2007
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