Quantum geometry from phase space reduction
Florian Conrady,Laurent Freidel +1 more
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TLDR
In this article, an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra is given. But the main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral of classical tetrahedral networks.Abstract:
In this work we give an explicit isomorphism between the usual spin network basis and the direct quantization of the reduced phase space of tetrahedra. The main outcome is a formula that describes the space of SU(2) invariant states by an integral over coherent states satisfying the closure constraint exactly, or equivalently, as an integral over the space of classical tetrahedra. This provides an explicit realization of theorems by Guillemin--Sternberg and Hall that describe the commutation of quantization and reduction. In the final part of the paper, we use our result to express the FK spin foam model as an integral over classical tetrahedra and the asymptotics of the vertex amplitude is determined.read more
Citations
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The Spin-Foam Approach to Quantum Gravity
TL;DR: In this paper, the present status of the spin-foam approach to the quantization of gravity is reviewed and a pedagogical presentation of new models for four-dimensional quantum gravity is paided to the recently introduced new models.
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Twisted geometries: A geometric parametrization of SU(2) phase space
Laurent Freidel,Simone Speziale +1 more
TL;DR: In this article, the authors show how to parametrize this phase space in terms of quantities describing the intrinsic and extrinsic geometry of the triangulation dual to the graph.
Journal ArticleDOI
Polyhedra in loop quantum gravity
TL;DR: In this article, it was shown that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in 3 : a polyhedron is uniquely described by the areas and normals to its faces.
Journal ArticleDOI
Asymptotic analysis of the EPRL four-simplex amplitude
TL;DR: In this paper, the semiclassical limit of a 4-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter was studied and a canonical choice of phase for the boundary state was introduced and was shown to be necessary to obtain the results.
Journal ArticleDOI
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude
TL;DR: In this article, the semiclassical limit of a four-simplex amplitude for a spin foam quantum gravity model with an Immirzi parameter was studied and a canonical choice of phase for the boundary state was introduced and was shown to be necessary to obtain the results.
References
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Book
Generalized Coherent States and Their Applications
TL;DR: In this paper, the authors define the notion of generalized coherent states and define a generalization of the Coherent State Representation T?(g) of the Heisenberg-Weyl Group.
BookDOI
The Analysis of Linear Partial Differential Operators I
TL;DR: In this article, the analysis of linear partial differential operators i distribution theory and fourier rep are a good way to achieve details about operating certain products using instruction manuals, which are clearlybuilt to give step-by-step information about how you ought to go ahead in operating certain equipments.
Book
Geometric Invariant Theory
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
Book
Symplectic Techniques in Physics
TL;DR: The geometry of the moment map and motion in a Yang-Mills field and the principle of general covariance have been studied in this paper, where they have been shown to be complete integrability and contractions of symplectic homogeneous spaces.