This award supports research to develop a new paradigm for totally constrained theories like Einstein's theory of general relativity at a classical and quantum level. The new approach consists in constructing discrete theories such that the continuum theory arises as a well defined continuum limit. The specific proposal for constructing the discrete theories, called "uniform discretizations" has several attractive features. In particular the discrete theories avoid many of the hard conceptual problems that complicate traditional approaches to quantum general relativity. Development a complete theory to reconcile general relativity as a classical theory of gravitation with the principles of quantum mechanics remains one of the major open questions of theoretical physics. The research program supported by this award represents one approach to this problem. The broader impacts of this project are aiding in the creation of scientific human resources through the training of students and postdoctoral researchers in the relativity group at Louisiana State University and the possibility that the techniques introduced here may have applicability in other areas of science as well.
