(2 + 1) covariant lattice theory and 't Hooft's formulation
Por:
Waelbroeck H., Zapata J.A.
Publicada:
1 ene 1996
Resumen:
We show that 't Hooft's representation of (2 + 1)-dimensional gravity in terms of flat polygonal tiles is closely related to a gauge-fixed version of the covariant Hamiltonian lattice theory, 't Hooft's gauge is remarkable in that it leads to a Hamiltonian which is a linear sum of vertex Hamiltonians, each of which is defined modulo 2?. A cyclic Hamiltonian implies that 'time' is quantized. However, it turns out that this Hamiltonian is constrained. If one chooses an internal time and solves this constraint for the 'physical Hamiltonian', the result is not a cyclic function. Even if one quantizes following Dirac, the 'internal time' observable does not acquire a discrete spectrum. We also show that in Euclidean three-dimensional lattice gravity, 'space' can be either discrete or continuous depending on the choice of quantization. Finally, we propose a generalization of 't Hooft's gauge for Hamiltonian lattice formulations of topological gravity dimension four. © 1996 IOP Publishing Ltd.
Filiaciones:
Waelbroeck H.:
Instituto de Ciencias Nucleares, UNAM, Circuito Exterior CU, México DF 04510, Mexico
Zapata J.A.:
Center for Gravitational Physics and Geometry, Department of Physics, Pennsylvania State University, University Park, PA 16802, United States
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