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Title:
Insights into classical and quantum gravity from Regge Calculus
Speaker:
Abstract:
A brief introduction to Regge Calculus where curved spaces are approximated by higher-dimensional polyhedra will be provided. The importance of the hybrid cells coupling the Voronoi and Delaunay lattices will be emphasized in developing the underlying structure of this discrete geometry. The orthogonality in these cells is used to analyze the discrete versions of the equations of general relativity and to better understand the nature of its approximate diffeomorphism structure and to reveal the gravitational degrees of freedom in the theory. The structure of these hybrid cells yields equations that appear to be less complex than their continuum counterparts. We will then develop the initial-value data and evolution for Regge Calculus and briefly highlight some numerical applications, including Ricci flow in 3D. We introduce a novel path integral for quantum gravity following motivation from A. D. Alexandrov. Following the words of J. A. Wheeler that “a theory in and of itself should in principle reveal what questions can and cannot be asked,” we seek a deeper interpretation of the propagator in quantum gravity.
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