Such a uniform shrinking of simplices is known to be necessary
in order for piecewise flat manifolds to approach their continuum
counterparts [82]. On the
-lattice, with the
l dl
-measure and
, they determined
for decreasing
f
. For small
k, the choice of
f
seems to have only little influence, but towards the transition
point
,
simultaneously decreases. Next they investigated a variety of
measures of the form
(see also [35]). For
, only a mild
-dependence of
is observed as
. However, for
, there are significant differences for the entire range of
k, and some evidence that the geometry degenerates.
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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 |