1996/11/13 by Alejandro Corichi, Jose A. Zapata, JoséA. Zapata
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Diffeomorphism #Gauge theory #Hamiltonian constraint #Homotopy and Cohomology in Algebraic Topology #Lattice (music) #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum #Quantum gravity #Wheeler–DeWitt equation #gr-qc
paper · pdf · doi:10.1016/s0550-3213(97)00141-7
published as Nucl.Phys. B493 (1997) 475-490 · 11 Pages, Revtex, 3 figures
arxiv created 1996/11/13 · openalex publication_date 1997/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices, one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider 2+1 gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known --for both the continuum and the lattice-- and can be compared.