Consistent discretization and canonical classical and quantum Regge calculus

We apply the consistent discretization'' technique to the Regge action for (Euclidean and Lorentzian) general relativity in arbitrary number of dimensions. The result is a well defined canonical theory that is free of constraints and where the dynamics is implemented as a canonical transformation. This provides a framework for the discussion of topology change in canonical quantum gravity. In the Lorentzian case, the framework appears to be naturally free of the spikes’’ that plague traditional formulations. It also provides a well defined recipe for determining the measure of the path integral.