SPIKES IN QUANTUM REGGE CALCULUS

For most measures in two-dimensional quantum Regge calculus proposed i n the literature we show that the average values of link lengths l, [l (n)], do not exist for sufficiently high powers of n. In particular, t his is also true for the nonlocal DeWitt-like measure introduced by Re gge and Lund. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This mi ght explain the failure of quantum Regge calculus to reproduce the con tinuum results of two-dimensional quantum gravity. It points to severe problems for the Regge approach in higher dimensions.