A Hamiltonian Lattice Theory for Homogeneous Curved Spacetimes in 2+1 Dimensions

dc.creatorCriscuolo, A.
dc.creatorWaelbroeck, H.
dc.date1996-01-19
dc.date.accessioned2026-07-07T03:30:59Z
dc.date.available2026-07-07T03:30:59Z
dc.descriptionWe propose an exact Hamiltonian lattice theory for (2+1)-dimensional spacetimes with homogeneous curvature. By gauging away the lattice we find a generalization of the ``polygon representation'' of (2+1)-dimensional gravity. We compute the holonomies of the Lorentz connection ${\bf A}_i = ω_i^a {\bf L}_a + e_i^a {\bf K}_a$ and find that the cycle conditions are satisfied only in the limit $Λ\to 0$. This implies that, unlike in (2+1)-dimensional Einstein gravity, the connection ${\bf A}$ is not flat. If one modifies the theory by taking the cycle conditions as constraints, then one finds that the constraints algebra is first-class only if the Poisson bracket structure is deformed. This suggests that a finite theory of quantum gravity would require either a modified action including higher-order curvature terms, or a deformation of the commutator structure of the metric observables.
dc.descriptionTeX file, 19 pages, please contact the author for figures
dc.identifierhttps://arxiv.org/abs/gr-qc/9601028
dc.identifierhttp://arxiv.org/abs/gr-qc/9601028
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/35709
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleA Hamiltonian Lattice Theory for Homogeneous Curved Spacetimes in 2+1 Dimensions
dc.typetext

Files

Collections