Year: 2006
Type: article
Abstract: In 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 are 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 explicitly compute the lowest order terms (in the self-interaction coupling constant λ) of the propagator and of the three-point function. Finally, we compute the lowest order quantum gravity corrections (in the Newton constant G ) to the propagator and to the three-point function.
Source: Classical and Quantum Gravity
Author: Karim Noui
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2053305876