Coherent state operators in loop quantum gravity

Alesci, Emanuele; Dapor, Andrea; Lewandowski, Jerzy; Mäkinen, Ilkka; Sikorski, Jan

doi:10.1103/physrevd.92.104023

Cited by 7 publications

(13 citation statements)

References 56 publications

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“…Since we desire to show how the semi-classical limit of these COs can be obtained, the best option is to use the so-called coherent-picture of operators recently introduced in Ref. [107]. This provides a representation of operators in the basis of semi-classical state vectors.…”

Section: Quantized Directions Imply Quantized Coordinatesmentioning

confidence: 99%

“…The SU (2) gauge invariance of coherent state operators has been discussed in some details in Ref. [107].…”

Section: Quantized Directions Imply Quantized Coordinatesmentioning

confidence: 99%

“…To some extent our work can be regarded as a concrete realization of that proposal. Using the action on semi-classical coherent states [104,105,107],…”

Section: Introductionmentioning

confidence: 99%

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Quantum coordinate operators: why space-time lattice is fuzzy

Brahma,

Marcianò,

Ronco

2017

Preprint

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Section: Quantized Directions Imply Quantized Coordinatesmentioning

confidence: 99%

“…The SU (2) gauge invariance of coherent state operators has been discussed in some details in Ref. [107].…”

Section: Quantized Directions Imply Quantized Coordinatesmentioning

confidence: 99%

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Quantum coordinate operators: why space-time lattice is fuzzy

Brahma,

Marcianò,

Ronco

2017

Preprint

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“…There are several approximation schemes that one could rely on. Namely, perturbative methods [17], semi-classical analysis [18], coherent states [19][20][21][22][23][24][25][26], effective dynamics for restricted sectors [27], or controlled truncations of the quantum degrees of freedom [28][29][30]. Each of these approaches contributed significantly in improving the understanding of the dynamics and the symmetric sectors in polymer quantum theories.…”

Section: Introductionmentioning

confidence: 99%

Polymer quantization of connection theories: Graph coherent states

Assanioussi

2018

Phys. Rev. D

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We present the construction of a new family of coherent states for quantum theories of connections obtained following the polymer quantization. The realization of these coherent states is based on the notion of graph change, in particular the one induced by the quantum dynamics in Yang-Mills and gravity quantum theories. Using a Fock-like canonical structure that we introduce, we derive the new coherent states that we call the graph coherent states. These states take the form of an infinite superposition of basis network states with different graphs. We further discuss the properties of such states and certain extensions of the proposed construction. *

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“…In the context of twisted geometries, this extra angle plays an important role and is used to encode the extrinsic curvature of the 3d hypersurface in the 4d space-time [4,15]. This actually was the starting point for the spinorial reformulation of loop quantum gravity [16][17][18][19][20][21], where the spinors become the label of coherent spin network states and the quantum gravity constraints are written as differential operators in those complex variables. In the context of the spinfoam framework providing a quantized path integral for discretized gravity (which can be interpreted as a history formulation of loop quantum gravity), these coherent spin network techniques have also been used to derive the semi-classical behavior of spinfoam amplitudes for large spin (i.e.…”

mentioning

confidence: 99%

Hamiltonian flows of Lorentzian polyhedra: Kapovich-Millson phase space and SU(1, 1) intertwiners

Livine

2019

Journal of Mathematical Physics

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We describe the Lorentzian version of the Kapovitch-Millson phase space for polyhedra with N faces. Starting with the Schwinger representation of the su(1, 1) Lie algebra in terms of a pair of complex variables (or spinor), we define the phase space for a space-like vectors in the threedimensional Minkowski space R 1,2 . Considering N copies of this space, quotiented by a closure constraint forcing the sum of those 3-vectors to vanish, we obtain the phase space for Lorentzian polyhedra with N faces whose normal vectors are space-like, up to Lorentz transformations. We identify a generating set of SU(1, 1)-invariant observables, whose flow by the Poisson bracket generate both area-preserving and area-changing deformations. We further show that the area-preserving observables form a gl N (R) Lie algebra and that they generate a GLN (R) action on Lorentzian polyhedra at fixed total area. That action is cyclic and all Lorentzian polyhedra can be obtained from a totally squashed polyhedron (with only two non-trivial faces) by a GLN (R) transformation. All those features carry on to the quantum level, where quantum Lorentzian polyhedra are defined as SU(1, 1) intertwiners between unitary SU(1, 1)-representations from the principal continuous series.Those SU(1, 1)-intertwiners are the building blocks of spin network states in loop quantum gravity in 3+1 dimensions for time-like slicing and the present analysis applies to deformations of the quantum geometry of time-like boundaries in quantum gravity, which is especially relevant to the study of quasi-local observables and holographic duality. I. INTRODUCTIONThe question of quantum gravity is a great physical motivation to explore the fundamental structures of geometry. From a conservative perspective, its goal can be understood as defining a intrinsically discrete notion of geometry, due to the introduction of the Planck length, while still carrying an action of the continuous group of diffeomoprhisms. This would achieve the quantization of geometry. Following this line of research, the loop quantum gravity framework proposes quantum states of 3d geometry and aims at describing their evolution thereby generating the 4d space-time (see [1-3] for reviews). For space-like 3d hypersurfaces, those spin network states are graphs dressed with algebraic data from the representation theory of the Lie group SU(2). These can be interpreted as discrete geometries, named "twisted geometries" generalizing Regge triangulations [4,5]. Their fundamental building blocks are SU(2) intertwiners, i.e. SU(2)-invariant states in the tensor product of SU(2) representations, that are understood as the quantum counterpart of 3d polyhedra [6][7][8]. These quantum polyhedra are then glued together to form a discrete quantum 3d geometry. The purpose of the present paper is to investigate the extension of the standard framework to time-like hypersurfaces, with spin network states made from SU(1, 1) intertwiners representing quantized Lorentzian polyhedra. This is directly applicable to loop quantum ...

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Coherent state operators in loop quantum gravity

Cited by 7 publications

References 56 publications

Quantum coordinate operators: why space-time lattice is fuzzy

Quantum coordinate operators: why space-time lattice is fuzzy

Polymer quantization of connection theories: Graph coherent states

Hamiltonian flows of Lorentzian polyhedra: Kapovich-Millson phase space and SU(1, 1) intertwiners

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