The Dynamics of Quantum Gravity

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A new paradigm for dealing with the dynamics of totally constrained theories like general relativity will continue to be developed both at a classical and quantum level. The paradigm consists in constructing discrete theories such that the continuum theory of interest arises as a well defined limit. The specific proposal for constructing the discrete theories, called "uniform discretizations" has several attractive features. In particular the discrete theories are free of constraints and therefore avoid many of the hard conceptual problems that complicate traditional quantum gravity, and nevertheless manage to provide a well defined limit in which one recovers the continuum theory of interest. A paradigm emerges that is analogous to that of lattice gauge theory, where discrete theories are used in a limiting procedure to define a continuum theory of interest. This approach has already been applied successfully in some situations where the space-time has some spatial dependence (i.e. more complicated than homogeneous cosmologies) but without genuine degrees of freedom, most notably providing a characterization of the complete space-time of a non-singular loop quantum gravity black hole. This NSF award will focus on applying the paradigm in situations of increasing complexity. This includes the collapse of scalar fields to form black holes and related models. It is also proposed to further other topics related to the dynamics of quantum gravity like the problem of time and the issue of measurement in quantum mechanics. This research program also aids in the creation of human resources in US physics through the training of a postdoctoral researcher and provides the possibility that the discretization techniques introduced here may have applicability in other areas of science and engineering as well.