How many quanta are there in a quantum spacetime?

Ariwahjoedi, Seramika; Kosasih, Jusak Sali; Rovelli, Carlo; Zen, Freddy P.

doi:10.1088/0264-9381/32/16/165019

Cited by 14 publications

(18 citation statements)

References 23 publications

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“…In this section, we are going to present the geometric interpretation of the discrete phase spaces and the integrated flux obervables. In particular, we will see that the integrated flux observables can be used to define macroscopic variables which will be important for the coarse graining of spin networks [47,48] and spin foams [49][50][51][52]. We will explain that the integrated (macroscopic) fluxes do not necessarily need to satisfy the Gauss constraints.…”

Section: Geometric Interpretationmentioning

confidence: 99%

Flux formulation of loop quantum gravity: classical framework

Dittrich¹,

Geiller²

2015

Class. Quantum Grav.

140

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We recently introduced a new representation for loop quantum gravity, which is based on the BF vacuum and is in this sense much nearer to the spirit of spin foam dynamics. In the present paper we lay out the classical framework underlying this new formulation. The central objects in our construction are the so-called integrated fluxes, which are defined as the integral of the electric field variable over surfaces of codimension one, and related in turn to Wilson surface operators. These integrated flux observables will play an important role in the coarse graining of states in loop quantum gravity, and can be used to encode in this context the notion of curvature-induced torsion. We furthermore define a continuum phase space as the modified projective limit of a family of discrete phase spaces based on triangulations. This continuum phase space yields a continuum (holonomy-flux) algebra of observables. We show that the corresponding Poisson algebra is closed by computing the Poisson brackets between the integrated fluxes, which have the novel property of being allowed to intersect each other.

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Section: Geometric Interpretationmentioning

confidence: 99%

Flux formulation of loop quantum gravity: classical framework

Dittrich¹,

Geiller²

2015

Class. Quantum Grav.

140

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“…We conclude that while W provides an interesting nonlinear definition of dilations in the compact phase space T * SU(2), with a well-behaved continuum limit, its generic incompatibility with the closure constraint hinders direct applications to classical dynamical models on a fixed graph. On the other hand, it could intervene interestingly in situations where the closure constraint is relaxed, such as in coarse graining [62,63] or in some spin foam models [35,36].…”

Section: Holonomy-flux Symplectic 'Dilatations'mentioning

confidence: 99%

Twisted geometries, twistors, and conformal transformations

Långvik

Speziale

2016

Phys. Rev. D

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The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a time-like direction singled out. The isomorphism depends on the Immirzi parameter γ, and reduces to the identity for γ = ∞. Using this twistorial representation we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a 1-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one -that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view, and compare it with a discretisation of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit its action has an interesting nonlinear structure, but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan, and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [2].

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“…In this section, we introduce two important sub-classes of coarse-grainings, both of which are closed under composition and naturally appear in some physical theories, such as loop quantum gravity [1], tensor network renormalization [3], etc. Definition 10.…”

Section: Vertex and Edge Coarse-grainingmentioning

confidence: 99%

Causal-net category

Lu¹

2022

Preprint

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A causal-net is a finite acyclic directed graph. In this paper, we introduce a category, denoted as Cau, whose objects are causal-nets and morphisms are functors of path categories of causal-nets. It is called causal-net category and in fact the Kleisli category of the "free category on a causal-net" monad. We study several composition-closed classes of morphisms in Cau, which characterize interesting causal-net relations, such as coarse-graining, contraction, immersion-minor, topological minor, etc., and prove several useful decomposition theorems. In addition, we show that the notions of a coloring and a minor can be understood as a special kind of minimal-quotient and sub-quotient in Cau, respectively. Base on these results, we conclude that Cau is a natural setting for studying causal-nets, and the theory of Cau should shed new light on the category-theoretic understanding of graph theory.

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How many quanta are there in a quantum spacetime?

Cited by 14 publications

References 23 publications

Flux formulation of loop quantum gravity: classical framework

Flux formulation of loop quantum gravity: classical framework

Twisted geometries, twistors, and conformal transformations

Causal-net category

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