Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory

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dc.creatorNoui, Karim
dc.date2006-12-22
dc.date.accessioned2026-07-07T11:21:37Z
dc.date.available2026-07-07T11:21:37Z
dc.descriptionIn a companion paper, we have emphasized the role of the Drinfeld double DSU(2) in the context of three dimensional Riemannian Loop Quantum Gravity coupled to massive spinless point particles. We make use of this result to propose a model for a self-gravitating quantum field theory (massive spinless non-causal scalar field) in three dimensional Riemannian space. We start by constructing the Fock space of the free self-gravitating field: the vacuum is the unique DSU(2) invariant state, one-particle states correspond to DSU(2) unitary irreducible simple representations and any multi-particles states is obtained as the symmetrized tensor product between simple representations. The associated quantum field is defined by the usual requirement of covariance under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential (the obtained model is a Group Field Theory) and compute explicitely the lowest order terms (in the self-interaction coupling constant $λ$) of the propagator and of the three-points function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G) to the propagator and to the three-points function.
dc.description36 pages, published in Class. Quant. Grav
dc.identifierhttps://arxiv.org/abs/gr-qc/0612145
dc.identifierhttp://arxiv.org/abs/gr-qc/0612145
dc.identifierClass.Quant.Grav.24:329-360,2007
dc.identifierdoi:10.1088/0264-9381/24/2/005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/194318
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleThree dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory
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