Spin networks and quantum gravity

Rovelli, Carlo; Smolin, Lee

doi:10.1103/physrevd.52.5743

Cited by 533 publications

(846 citation statements)

References 48 publications

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“…For the graph F these nodes are expanded into three-valent nodes. Thus a B 2 basis can be identified as a quantum deformed spin network basis [18,51,52,[72][73][74]. This allows us to define a (Ashtekar-Lewandowski like) vacuum state (on a fixed triangulation), by assigning only trivial labels also for the under-crossing graph F u in the B 2 basis.…”

Section: Jhep05(2017)123mentioning

confidence: 99%

“…These are associated to the one-skeleton of the triangulation and the one-skeleton of the dual complex respectively. The latter basis coincides 4 with a (quantum deformed) spin network basis [51,52], which diagonalizes (spatial) geometry operators, such as the areas of the triangles. The dual basis is associated to the one-skeleton of the triangulation and can be interpreted as encoding the curvature (in excess of the homogeneous curvature) concentrated on this one-skeleton.…”

Section: Jhep05(2017)123mentioning

confidence: 99%

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(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

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We apply the recently suggested strategy to lift state spaces and operators for (2 + 1)-dimensional topological quantum field theories to state spaces and operators for a (3 + 1)-dimensional TQFT with defects. We start from the (2 + 1)-dimensional TuraevViro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects.This work has important applications for quantum gravity as well as the theory of topological phases in (3 + 1) dimensions. It provides a self-dual quantum geometry realization based on a vacuum state peaked on a homogeneously curved geometry. The state spaces and operators we construct here provide also an improved version of the Walker-Wang model, and simplify its analysis considerably.We in particular show that the fusion bases of the (2 + 1)-dimensional theory lead to a rich set of bases for the (3 + 1)-dimensional theory. This includes a quantum deformed spin network basis, which in a loop quantum gravity context diagonalizes spatial geometry operators. We also obtain a dual curvature basis, that diagonalizes the Walker-Wang Hamiltonian.Furthermore, the construction presented here can be generalized to provide state spaces for the recently introduced dichromatic four-dimensional manifold invariants.

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Section: Jhep05(2017)123mentioning

confidence: 99%

Section: Jhep05(2017)123mentioning

confidence: 99%

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Dittrich

2017

J. High Energ. Phys.

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“…In the present short note, we rather regard it as a space. This might be similar in spirit to the idea of brane world [5,6] and also to the network appearing in quantum gravity [7,8,9,10,11]. We shall discuss the low frequency propagation modes on it.…”

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confidence: 98%

“…The numerical factor is determined from (9). Thus, also from (12), we obtain the effective Lagrangian…”

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confidence: 99%

Low-energy propagation modes on string network

Sasakura¹

2001

J. High Energy Phys.

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We study low-energy propagation modes on string network lattice. Specifically, we consider an infinite two-dimensional regular hexagonal string network and analyze the low frequency propagation modes on it. The fluctuation modes tangent to the two-dimensional plane respect the spatial rotational symmetry on the plane, and are described by Maxwell theory. The gauge symmetry comes from the marginal deformation of changing the sizes of the loops of the lattice. The effective Lorentz symmetry respected at low energy will be violated at high energy. *

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“…Spinors are automatically present because of the polyvector character of the basic quantities X and V . There is very probably a deep relationship between this approach and the ones known as loop quantum gravity [70], spin networks [71], and spin foams [72], pioneered by Smolin, Rovelli and Baez, to name just few. I beleive that in this book we have an outline of a possible general, unifying, background independent geometrical principle behind many of the approaches incorporating strings, p-branes, and quantum gravity.…”

Section: The Landscape Of Theoretical Physics: a Global Viewmentioning

confidence: 99%

The Landscape of Theoretical Physics: A Global View

Pavšič¹

2002

Fundamental Theories of Physics

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This is a book for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description of geometry by means of Clifford algebra, about the fascinating possibilities the latter algebra offers in reformulating the existing physical theories, and quantizing them in a natural way. It is shown how Clifford algebra provides much more: it provides room for new physics, with the prospects of resolving certain long standing puzzles. The theory of branes and the idea of how a 3-brane might represent our world is discussed in detail. Much attention is paid to the elegant geometric theory of branes which employs the infinite dimensional space of functions describing branes. Clifford algebra is generalized to the infinite dimensional spaces. In short, this is a book for anybody who would like to explore how the "theory of everything" might possibly be formulated. The theory that would describe all the known phenomena, could not be formulated without taking into account "all" the theoretical tools which are available. Foundations of those tools and their functional interrelations are described in the book. Note: This book was published by Kluwer Academic Publishers in 2001.The body of the posted version is identical to the published one, except for corrections of misprints, and some minor revisions that I have found necessary.

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Spin networks and quantum gravity

Cited by 533 publications

References 48 publications

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

(3 + 1)-dimensional topological phases and self-dual quantum geometries encoded on Heegaard surfaces

Low-energy propagation modes on string network

The Landscape of Theoretical Physics: A Global View

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