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Quantum Gravity at the Corner

Perimeter Institute for Theoretical Physics, Waterloo, ON N2L-2Y5, Canada
Aix Marseille University, Université de Toulon, CNRS, CPT, 13288 Marseille, France
Author to whom correspondence should be addressed.
Universe 2018, 4(10), 107;
Received: 17 July 2018 / Revised: 2 October 2018 / Accepted: 10 October 2018 / Published: 15 October 2018
PDF [927 KB, uploaded 15 October 2018]


We investigate the quantum geometry of a 2d surface S bounding the Cauchy slices of a 4d gravitational system. We investigate in detail for the first time the boundary symplectic current that naturally arises in the first-order formulation of general relativity in terms of the Ashtekar–Barbero connection. This current is proportional to the simplest quadratic form constructed out of the pull back to S of the triad field. We show that the would-be-gauge degrees of freedo arising from S U ( 2 ) gauge transformations plus diffeomorphisms tangent to the boundary are entirely described by the boundary 2-dimensional symplectic form, and give rise to a representation at each point of S of S L ( 2 , R ) × S U ( 2 ) . Independently of the connection with gravity, this system is very simple and rich at the quantum level, with possible connections with conformal field theory in 2d. A direct application of the quantum theory is modelling of the black horizons in quantum gravity. View Full-Text
Keywords: non perturbative quantum gravity; loop quantum gravity; general relativity non perturbative quantum gravity; loop quantum gravity; general relativity

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Freidel, L.; Perez, A. Quantum Gravity at the Corner. Universe 2018, 4, 107.

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