Spikes in Quantum Regge Calculus
J. Ambjorn, J. Nielsen, J. Rolf, G. Savvidy
Abstract
We demonstrate by explicit calculation of the DeWitt-like measure in two-dimensional quantum Regge gravity that it is highly non-local and that the average values of link lengths l, <ln>, do not exist for sufficient high powers of n. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This might explain the failure of quantum Regge calculus to reproduce the continuum results of two-dimensional quantum gravity. It points to severe problems for the Regge approach in higher dimensions.
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