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พฤศจิกายน 2553

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13 พฤศจิกายน 2553

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U(N) tools for Loop Quantum Gravity: The Return of the Spinor
Authors: Enrique F. Borja, Laurent Freidel, Iñaki Garay, Etera R. Livine
(Submitted on 26 Oct 2010)
Abstract: We explore the classical setting for the U(N) framework for SU(2) intertwiners for loop quantum gravity (LQG) and describe the corresponding phase space in terms of spinors with appropriate constraints. We show how its quantization leads back to the standard Hilbert space of intertwiner states defined as holomorphic functionals. We then explain how to glue these intertwiners states in order to construct spin network states as wave-functions on the spinor phase space. In particular, we translate the usual loop gravity holonomy observables to our classical framework. Finally, we propose how to derive our phase space structure from an action principle which induces non-trivial dynamics for the spin network states. We conclude by applying explicitly our framework to states living on the simple 2-vertex graph and discuss the properties of the resulting Hamiltonian.
Comments: 23 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph)
Cite as: arXiv:1010.5451v1 [gr-qc]

Critical Overview of Loops and Foams
Authors: Sergei Alexandrov, Philippe Roche
(Submitted on 22 Sep 2010)
Abstract: This is a review of the present status of loop and spin foam approaches to quantization of four-dimensional general relativity. It aims at raising various issues which seem to challenge some of the methods and the results often taken as granted in these domains. A particular emphasis is given to the issue of diffeomorphism and local Lorentz symmetries at the quantum level and to the discussion of new spin foam models. We also describe modifications of these two approaches which may overcome their problems and speculate on other promising research directions.
Comments: 75 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Report number: LPTA:10-063
Cite as: arXiv:1009.4475v1 [gr-qc]

From twistors to twisted geometries(***)
Authors: Laurent Freidel, Simone Speziale
(Submitted on 1 Jun 2010)
Abstract: In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph. Here we unravel the origin of the phase space from a geometric interpretation of twistors.
Comments: 9 pages
Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
Journal reference: Phys.Rev.D82:084041,2010
DOI: 10.1103/PhysRevD.82.084041
Cite as: arXiv:1006.0199v1 [gr-qc]

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