Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 8 (2012), 002, 29 pages      arXiv:1111.1879
Contribution to the Special Issue “Loop Quantum Gravity and Cosmology”

Discretisations, Constraints and Diffeomorphisms in Quantum Gravity

Benjamin Bahr a, Rodolfo Gambini b and 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

Received November 09, 2011, in final form December 31, 2011; Published online January 08, 2012

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.

Key words: quantum gravity; diffeomorphisms; constraints; consistent discretizations; gauge symmetries; perfect actions; renormalization.

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