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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We investigate the construction of coherent states for quantum theories of
connections based on graphs embedded in a spatial manifold, as in loop quantum
gravity. We discuss the many subtleties of the construction, mainly related to
the diffeomorphism invariance of the theory. Aiming at approximating a
continuum geometry in terms of discrete, graph-based data, we focus on coherent
states for collective observables characterizing both the intrinsic and
extrinsic geometry of the hypersurface, and we argue that one needs to revise
accordingly the more local definitions of coherent states considered in the
literature so far. In order to clarify the concepts introduced, we work through
a concrete example that we hope will be useful to applying coherent state
techniques to cosmology.
