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doi:10.1016/0550-3213(89)90623-8 
Copyright © 1989 Published by Elsevier B.V.
On the continuum limit of curvature squared actions in the Regge calculus
Received 24 June 1988;
revised 28 November 1988.
Available online 18 October 2002.
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Abstract
We evaluate the continuum limit of a family of curvature squared actions for the Regge calculus proposed by Hamber and Williams. The answers depend on how the continuum limit is defined. When the link lengths are defined as the distance in an embedding space between the endpoints of the link, we find that no member of this family approaches the continuum limit correctly. Defining the link lenghts as the length of a geodesic between the endpoints of the link, we find that a unique member is selected, and we prove for the general two dimensional compact manifold that this Regge calculus action converges to ∫R2√gd2x.
