Programme Speaker: Prof. Rodolfo Gambini Title: Consistent discretizations of totally constrained systems Abstract: I describe the consistent discretization scheme for the quantization of totally constrained systems and quantum gravity. As a first example I analyze the canonical formalism for Regge Calculus. I complete all the steps of the program for a reparameterization invariant system composed by a microscopic particle in a potential and a macroscopic clock. I define the physical Hilbert space of the discrete totally constrained theories, and I study the quantum evolution given by conditional probabilities defined in terms of quantum magnitudes associated to the clock and the system. I show how to recover the standard quantum mechanical continuum limit for the microscopic system. Talk: Transparencies, Recorded Talk