New insights in quantum geometry
arXiv:1112.1781 · doi:10.1088/1742-6596/360/1/012007
Abstract
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a brief description of the main structures and results of quantum geometry, I review a new description of the quantized geometry in terms of polyhedra, new results on the volume operator, and a way to incorporate a classical background metric into the quantum description. Finally I describe a new type of exponentiated flux operator, and its application to Chern-Simons theory and black holes.
10 pages, 3 figures; Proceedings of Loops'11, Madrid, submitted to Journal of Physics: Conference Series (JPCS)
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