1993/11/30 by Henri Waelbroeck, José A. Zapata, Jose Antonio Zapata · 4 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Curvature #Gauge theory #Geometry #Hamiltonian (control theory) #Hamiltonian lattice gauge theory #Homogeneous space #Lattice field theory #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Theoretical physics #Topology (electrical circuits) #gr-qc
paper · pdf · doi:10.1088/0264-9381/11/4/015
published as Class.Quant.Grav.11:989-998,1994 · 15 pages, Mexico preprint ICN-UNAM-93-13
arxiv created 1993/11/30 · openalex publication_date 1994/04/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Topological gravity is the reduction of Einstein's theory to spacetimes with vanishing curvature, but with global degrees of freedom related to the topology of the universe. We present an exact Hamiltonian lattice theory for topological gravity, which admits translations of the lattice sites as a gauge symmetry. There are additional symmetries, not present in Einstein's theory, which kill the local degrees of freedom. We show that these symmetries can be fixed by choosing a gauge where the torsion is equal to zero. In this gauge, the theory describes flat spacetimes. We propose two methods to advance towards the holy grail of lattice gravity: a Hamiltonian lattice theory for curved spacetimes, with first-class translation constraints.