$2+1$ Covariant Lattice Theory and t'Hooft's Formulation

Details $2+1$ Covariant Lattice Theory and t'Hooft's Formulation $2+1$ Covariant Lattice Theory and t'Hooft's Formulation

1996-01-09

arxiv.org/abs/gr-qc/9601011v1

Class.Quant.Grav. 13 (1996) 1761-1768

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages of text. One figure available from J.A. Zapata upon request

Scientific paper

10.1088/0264-9381/13/7/009

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 $2 \pi$. A cyclic Hamiltonian implies that ``time'' is quantized. However, it turns out that this Hamiltonian is {\it 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 {\it a la Dirac}, the ``internal time'' observable does not acquire a discrete spectrum. We also show that in Euclidean 3-d 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 4.

Affiliated with

Also associated with

No associations

Rating

$2+1$ Covariant Lattice Theory and t'Hooft's Formulation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with $2+1$ Covariant Lattice Theory and t'Hooft's Formulation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and $2+1$ Covariant Lattice Theory and t'Hooft's Formulation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-713479