A Hamiltonian Lattice Theory for Homogeneous Curved Spacetimes in 2+1 Dimensions
| dc.creator | Criscuolo, A. | |
| dc.creator | Waelbroeck, H. | |
| dc.date | 1996-01-19 | |
| dc.date.accessioned | 2026-07-07T03:30:59Z | |
| dc.date.available | 2026-07-07T03:30:59Z | |
| dc.description | We 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.description | TeX file, 19 pages, please contact the author for figures | |
| dc.identifier | https://arxiv.org/abs/gr-qc/9601028 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/9601028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/35709 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | A Hamiltonian Lattice Theory for Homogeneous Curved Spacetimes in 2+1 Dimensions | |
| dc.type | text |