Benjamin Bahr, Rodolfo Gambini, Jorge Pullin, “Discretisations, constraints and diffeomorphisms in quantum gravity”, SIGMA, 2012, Volume 8,002, 29 pp.

This article is cited in 19 papers

Discretisations, constraints and diffeomorphisms in quantum gravity

Benjamin Bahr^a, Rodolfo Gambini^b, Jorge Pullin^c

^a Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
^b Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400 Montevideo, Uruguay
^c Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803-4001, USA

Abstract: In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application of the master constraint program to construct the physical Hilbert space of the canonical theory, as well as the Perfect Actions approach, which aims at finding a path integral measure with the correct symmetry behavior under diffeomorphisms.

Keywords: quantum gravity, diffeomorphisms, constraints, consistent discretizations, gauge symmetries, perfect actions, renormalization.

MSC: 37M99; 70H45; 81T17; 82B28; 83C27; 83C45

Received: November 9, 2011; in final form December 31, 2011; Published online January 8, 2012

Language: English

DOI: 10.3842/SIGMA.2012.002