Addendum to ‘EPRL/FK asymptotics and the flatness problem’

Engle, Jonathan; Kamiński, Wojciech; Oliveira, José

doi:10.1088/1361-6382/abf897

Cited by 18 publications

(11 citation statements)

References 22 publications

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“…The accidental flatness constraint is consistent with the above argument about over-constrained equations, and it has been demonstrated explicitly in the example well-studied in, e.g., [12,36]. If one only considers the real critical point for the dominant contribution to A(K), Eq.…”

Section: Complex Critical Point and Effective Dynamicssupporting

confidence: 76%

Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-$Δ_3$ complex

Han¹,

Liu²,

Qu³

2023

Preprint

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The complex critical points are analyzed in the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model in the large-j regime. For the 4-simplex amplitude, taking into account the complex critical point generalizes the large-j asymptotics to the situation with non-Regge boundary data and relates to the twisted geometry. For generic simplicial complexes, we present a general procedure to derive the effective theory of Regge geometries from the spinfoam amplitude in the large-j regime by using the complex critical points. The effective theory is analyzed in detail for the spinfoam amplitude on the double-∆ 3 simplicial complex. We numerically compute the effective action and the solution of the effective equation of motion on the double-∆ 3 complex. The effective theory reproduces the classical Regge gravity when the Barbero-Immirzi parameter γ is small.

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Section: Complex Critical Point and Effective Dynamicssupporting

confidence: 76%

Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-$Δ_3$ complex

Han¹,

Liu²,

Qu³

2023

Preprint

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“…The same conclusion can also be derived using saddle point techniques, and Poisson resummation [43]. We preferred to follow the singular support argument to demystify the result of [23] because it focuses more on the holonomies than the geometries.…”

Section: Extended Eprl Spin Foam Amplitudesmentioning

confidence: 89%

“…The "naive" flatness problem [40,41,42,23,43] claims that, at fixed triangulation, the amplitude is dominated in the large (boundary) spin limit by flat geometries. For a path integral formulation of a quantum theory, the amplitude is exponentially suppressed if and only if the boundary data is inconsistent with the classical equation of motions.…”

Section: Extended Eprl Spin Foam Amplitudesmentioning

confidence: 99%

Geometry from local flatness in Lorentzian spin foam theories

Donà¹

2022

Preprint

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Local flatness is a property shared by all the spin foam models. It ensures that the theory's fundamental building blocks are flat by requiring locally trivial parallel transport. In the context of simplicial Lorentzian spin foam theory, we show that local flatness is the main responsible for the emergence of geometry independently of the details of the spin foam model. We discuss the asymptotic analysis of the EPRL spin foam amplitudes in the large quantum number regime, highlighting the interplay with local flatness.

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“…The EPRL-FK model [1,2] (we will refer to it as just EPRL for brevity) is the stateof-the-art spin foam model. There is a large consensus in the community [3][4][5][6][7] that the classical continuum theory can be recovered with a double limit of finer discretization and vanishing h. This observation is supported by the emergence of Regge geometries and the Regge action in the asymptotics of the 4-simplex vertex amplitude for large quantum numbers [8,9] and the recent study of many vertices transition amplitudes.…”

Section: Introductionmentioning

confidence: 97%

How-to Compute EPRL Spin Foam Amplitudes

Donà¹,

Frisoni

2022

Universe

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Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but the entry barrier is steep, mainly because of its unusual language and notions scattered around the literature. This paper is a pedagogical guide to spin foam transition amplitude calculations. We show how to write an EPRL-FK transition amplitude, from the definition of the 2-complex to its numerical implementation using sl2cfoam-next. We guide the reader using an explicit example balancing mathematical rigor with a practical approach. We discuss the advantages and disadvantages of our strategy and provide a novel look at a recently proposed approximation scheme.

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Addendum to ‘EPRL/FK asymptotics and the flatness problem’

Cited by 18 publications

References 22 publications

Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-$Δ_3$ complex

Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-$Δ_3$ complex

Geometry from local flatness in Lorentzian spin foam theories

How-to Compute EPRL Spin Foam Amplitudes

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