caa a22 4500 445386541 CHVBK 20180317143033.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s10714-010-1095-0 doi (NATIONALLICENCE)springer-10.1007/s10714-010-1095-0 Quantum geometry from 2+1 AdS quantum gravity on the torus [Elektronische Daten] [J. Nelson, R. Picken] Wilson observables for 2 + 1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices. Springer Science+Business Media, LLC, 2010 Wilson observables nationallicence 2+1 Quantum gravity nationallicence Goldman bracket nationallicence Area phases nationallicence Nelson J. Dipartimento di Fisica Teorica, Università degli Studi di Torino, via Pietro Giuria 1, 10125, Turin, Italy aut Picken R. Departamento de Matemática, Instituto Superior Técnico, Technical University of Lisbon, Avenida Rovisco Pais, 1049-001, Lisbon, Portugal aut General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/3(2011-03-01), 777-795 0001-7701 43:3<777 2011 43 10714 https://doi.org/10.1007/s10714-010-1095-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-010-1095-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nelson J. Dipartimento di Fisica Teorica, Università degli Studi di Torino, via Pietro Giuria 1, 10125, Turin, Italy aut NATIONALLICENCE 700 1- Picken R. Departamento de Matemática, Instituto Superior Técnico, Technical University of Lisbon, Avenida Rovisco Pais, 1049-001, Lisbon, Portugal aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/3(2011-03-01), 777-795 0001-7701 43:3<777 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer