T G Budd and R Loll 2009 Class. Quantum Grav. 26 185011 doi:10.1088/0264-9381/26/18/185011
T G Budd and R Loll
Show affiliationsInspired by previous work in (2 + 1)-dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian gravity with vanishing cosmological constant and spatially compact universes of genus g ≥ 2. Taking the Chern–Simons formulation with the Poincaré gauge group as our starting point, we identify a set of length variables corresponding to space- and timelike distances along geodesics in three-dimensional Minkowski space. These are Dirac observables, that is, functions on the reduced phase space, whose quantization is essentially unique. For both space- and timelike distance operators, the spectrum is continuous and not bounded away from zero.
04.60.Kz Lower dimensional models; minisuperspace models
81V17 Gravitational interaction (See also 83Cxx and 83Exx)
83C45 Quantization of the gravitational field
81S10 Geometry and quantization, symplectic methods (See also 53D50)
Issue 18 (21 September 2009)
Received 19 June 2009
Published 7 September 2009
T G Budd and R Loll 2009 Class. Quantum Grav. 26 185011
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