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Dec8-11, 08:23 PM
Sci Advisor
PF Gold
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P: 23,274
Deformed General Relativity and Effective Actions from Loop Quantum Gravity
Martin Bojowald, George M. Paily
(Submitted on 8 Dec 2011)
Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to effective constraints of canonical quantum gravity and applied to model systems as well as general metrics, with the following conclusions:
(i) Dispersion relations of matter and gravitational waves are deformed in related ways, ensuring a consistent realization of causality.
(ii) Inverse-triad corrections modify the classical action in a way clearly distinguishable from curvature effects. In particular, these corrections can be significantly larger than often expected for standard quantum-gravity phenomena.
(iii) Finally, holonomy corrections in high-curvature regimes do not signal the evolution from collapse to expansion in a "bounce," but rather the emergence of the universe from Euclidean space at high density. This new version of signature-change cosmology suggests a natural way of posing initial conditions, and a solution to the entropy problem.
44 pages
New insights in quantum geometry
Hanno Sahlmann
(Submitted on 8 Dec 2011)
Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a brief description of the main structures and results of quantum geometry, I review a new description of the quantized geometry in terms of polyhedra, new results on the volume operator, and a way to incorporate a classical background metric into the quantum description. Finally I describe a new type of exponentiated flux operator, and its application to Chern-Simons theory and black holes.
10 pages, 3 figures; Proceedings of Loops'11, Madrid, submitted to Journal of Physics: Conference Series (JPCS)
Non-commutative holonomies in 2+1 LQG and Kauffman's brackets
Karim Noui, Alejandro Perez, Daniele Pranzetti
(Submitted on 8 Dec 2011)
We investigate the canonical quantization of 2+1 gravity with Λ > 0 in the canonical framework of LQG. A natural regularization of the constraints of 2+1 gravity can be defined in terms of the holonomies of A = A √Λe, where the SU(2) connection A and the triad field e are the conjugated variables of the theory. As a first step towards the quantization of these constraints we study the canonical quantization of the holonomy of the connection Aλ = A + λe acting on spin network links of the kinematical Hilbert space of LQG. We provide an explicit construction of the quantum holonomy operator, exhibiting a close relationship between the action of the quantum holonomy at a crossing and Kauffman's q-deformed crossing identity. The crucial difference is that the result is completely described in terms of standard SU(2) spin network states.
4 pages; Proceedings of Loops'11, Madrid, to appear in Journal of Physics: Conference Series (JPCS)

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