for local observables
, with
denoting the geodesic distance with respect to the metric
. There is an ambiguity in defining the
connected
part of the correlator (25
), as was pointed out by de Bakker and Smit [91,
92]. Contrary to expectations, after subtraction of the square of
the curvature expectation value, the resulting quantity
does not scale to zero with large distances. They therefore
proposed an alternative definition of the connected two-point
function, by subtracting the square of a ``curvature-to-nothing''
correlator
. This definition was compared in more detail by Bialas [45] with a more conventional notion, as, for example, the one used
in [48]. For the case of curvature correlators, their behaviour differs
significantly, especially at short distances.
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Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll http://www.livingreviews.org/lrr-1998-13 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |