Critical Behavior in Simplicial Quantum Gravity

Four-dimensional quantum gravity is a complex theory due to the unboundedness of the pure gravitational action, its non-renormalizability and non-polynomial nature 1. We will concentrate here on the simplicial formulation of quantum gravity also known as Regge calculus (for a review, see refs. 2,3). One of the advantages of the approach lies in the fact that it can be formulated in any space-time dimension (including the physically relevant case of four dimensions), and that it can be shown to be classically equivalent to general relativity. Furthermore the correspondence between lattice and continuum quantities is clear, and the interpretation of the terms in the action as well as the identification and separation of, for example, the measure contribution is'unambiguous 4-1°. For a more complete list of early references, see refs. 2,3