A spin foam model for general Lorentzian 4-geometries

Conrady, Florian; Hnybida, Jeff

doi:10.1088/0264-9381/27/18/185011

Cited by 46 publications

(123 citation statements)

References 41 publications

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“…[32] and [33], and we will see in Sec. V F that those states indeed can be associated to timelike faces 6 .…”

Section: Timelike Facesmentioning

confidence: 74%

“…Furthermore, let us point out that if we compare our approach with the coherent state approach used in Refs. [32] and [33], where it was stated that it is necessary to diagonalize a noncompact generator K 1 or K 2 instead of L 3 , in order to be able to describe timelike faces, we do not find this to be necessary, which makes our considerations more comprehensible.…”

Section: Quantization and Timelike Spin Networkmentioning

confidence: 97%

“…However, since we have seen that under the Hodge dual the bivector norm changes its sign, we can use this to distinguish the simplicity constraints for spacelike from those for timelike 2-surfaces. This essentially corresponds to the necessity of choosing another auxiliary vector U I to distinguish those two cases in the Conrady-Hnybida construction [32,33].…”

Section: Twistorial Description Of Timelike Hypersurfacesmentioning

confidence: 99%

“…This was also used in Refs. [32] and [33]. For that reason, we briefly review some representation theory of SU(1, 1) in the following section.…”

Section: Quantization and Timelike Spin Networkmentioning

confidence: 99%

“…How to connect those states (when j = −k for the discrete series) can be found in Refs. [32] and [33] or [60].…”

Section: B Spacelike Facesmentioning

confidence: 99%

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Timelike twisted geometries

Rennert

2017

Phys. Rev. D

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Within the twistorial parametrization of loop quantum gravity, we investigate the consequences of choosing a spacelike normal vector in the linear simplicity constraints. The amplitudes for the SU(2) boundary states of loop quantum gravity, given by most of the current spin foam models, are constructed in such a way that even in the bulk only spacelike building blocks occur. Using a spacelike normal vector in the linear simplicity constraints allows us to distinguish spacelike from timelike 2-surfaces. We propose in this paper a quantum theory that includes both spatial and temporal building blocks and hence a more complete picture of quantum spacetime. At the classical level, we show how we can describe T * SU(1, 1) as a symplectic quotient of 2-twistor space T 2 by area matching and simplicity constraints. This provides us with the underlying classical phase space for SU(1, 1) spin networks describing timelike boundaries and their extension into the bulk. Applying a Dirac quantization, we show that the reduced Hilbert space is spanned by SU(1, 1) spin networks and hence is able to give a quantum description of both spacelike and timelike faces. We discuss in particular the spectrum of the area operator and argue that for spacelike and timelike 2-surfaces it is discrete.

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“…[32] and [33], and we will see in Sec. V F that those states indeed can be associated to timelike faces 6 .…”

Section: Timelike Facesmentioning

confidence: 74%

Section: Quantization and Timelike Spin Networkmentioning

confidence: 97%

Section: Twistorial Description Of Timelike Hypersurfacesmentioning

confidence: 99%

“…This was also used in Refs. [32] and [33]. For that reason, we briefly review some representation theory of SU(1, 1) in the following section.…”

Section: Quantization and Timelike Spin Networkmentioning

confidence: 99%

“…How to connect those states (when j = −k for the discrete series) can be found in Refs. [32] and [33] or [60].…”

Section: B Spacelike Facesmentioning

confidence: 99%

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Timelike twisted geometries

Rennert

2017

Phys. Rev. D

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Spin Foams: Foundations

Engle,

Speziale

2023

Handbook of Quantum Gravity

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Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models

Marchetti

Oriti

Pithis

et al. 2023

J. High Energ. Phys.

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In the tensorial group field theory (TGFT) approach to quantum gravity, the basic quanta of the theory correspond to discrete building blocks of geometry. It is expected that their collective dynamics gives rise to continuum spacetime at a coarse grained level, via a process involving a phase transition. In this work we show for the first time how phase transitions for realistic TGFT models can be realized using Landau-Ginzburg mean-field theory. More precisely, we consider models generating 4-dimensional Lorentzian triangulations formed by spacelike tetrahedra the quantum geometry of which is encoded in non-local degrees of freedom on the non-compact group SL(2, ℂ) and subject to gauge and simplicity constraints. Further we include ℝ-valued variables which may be interpreted as discretized scalar fields typically employed as a matter reference frame. We apply the Ginzburg criterion finding that fluctuations around the non-vanishing mean-field vacuum remain small at large correlation lengths regardless of the combinatorics of the non-local interaction validating the mean-field theory description of the phase transition. This work represents a first crucial step to understand phase transitions in compelling TGFT models for quantum gravity and paves the way for a more complete analysis via functional renormalization group techniques. Moreover, it supports the recent extraction of effective cosmological dynamics from TGFTs in the context of a mean-field approximation.

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A spin foam model for general Lorentzian 4-geometries

Cited by 46 publications

References 41 publications

Timelike twisted geometries

Timelike twisted geometries

Spin Foams: Foundations

Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models

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