4.15 Summary4 Dynamical triangulations4.13 Exploring geometric properties

4.14 Two-point functions

It is possible to define two-point correlation functions on random geometries [16, 14], which are to be thought of as the discrete analogues of formal continuum correlators

  equation884

for local observables tex2html_wrap_inline3129, with tex2html_wrap_inline3131 denoting the geodesic distance with respect to the metric tex2html_wrap_inline3133 . There is an ambiguity in defining the connected part of the correlator (25Popup Equation), 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 tex2html_wrap_inline3135 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 tex2html_wrap_inline3137 . 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.



4.15 Summary4 Dynamical triangulations4.13 Exploring geometric properties

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