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Abstract: Wilson observables for 2+1 quantum gravity with negative cosmologicalconstant, when the spatial manifold is a torus, exhibit several novel features:signed area phases relate the observables assigned to homotopic loops, andtheir commutators describe loop intersections, with properties that are not yetfully understood. We describe progress in our study of this bracket, which canbe interpreted as a q-deformed Goldman bracket, and provide a geometricalinterpretation in terms of a quantum version of Pick-s formula for the area ofa polygon with integer vertices.



Author: J. E. Nelson, R. F. Picken

Source: https://arxiv.org/







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