Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2012-02-02
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, 1 figure
Scientific paper
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.
Oriti Daniele
Pereira Roberto
Sindoni Lorenzo
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