3.6 Evidence for a second-order 3 Quantum Regge Calculus3.4 The phase structure

3.5 Influence of the measure

For the pure Einstein action, (12Popup Equation) with tex2html_wrap_inline2575, some differences between the tex2html_wrap_inline2577 - and the tex2html_wrap_inline2579 -measure were investigated on a tex2html_wrap_inline2283 -lattice by Beirl et al [29, 30]. A constant-volume constraint was used for simulations with the tex2html_wrap_inline2583 -measure, and a cutoff tex2html_wrap_inline2585 for tex2html_wrap_inline2587 . A study of the k -dependence of bulk geometric quantities agreed with previous simulations, wherever applicable. For small k, both measures lead essentially to identical results. For the tex2html_wrap_inline2583 -measure only, one finds that tex2html_wrap_inline2595 and tex2html_wrap_inline2597 exhibit a jump at some tex2html_wrap_inline2599, due to the formation of spikes (isolated long link lengths, with the areas staying small). >From this, and the study of edge length distributions, one concludes that the DeWitt-type measure tex2html_wrap_inline2587 is generally better behaved.

3.6 Evidence for a second-order 3 Quantum Regge Calculus3.4 The phase structure

image Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll
http://www.livingreviews.org/lrr-1998-13
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