The Feynman propagator for quantum gravity: spin foams, proper time, orientation, causality and timeless-ordering

Oriti, Daniele

doi:10.1590/s0103-97332005000300019

Cited by 7 publications

(5 citation statements)

References 16 publications

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“…Furthermore the Ponzano Regge model includes in addition also a sum over orientations, which we do not consider here. The question arises, whether this result can be extended to the full non-linear theory and shed light on the problem, whether to include a sum over orientations into a quantum gravity path integral or not [57,58].…”

Section: Discussionmentioning

confidence: 99%

Path integral measure and triangulation independence in discrete gravity

2012

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A path integral measure for gravity should also preserve the fundamental symmetry of general relativity, which is diffeomorphism symmetry. In previous work, we argued that a successful implementation of this symmetry into discrete quantum gravity models would imply discretization independence. We therefore consider the requirement of triangulation independence for the measure in (linearized) Regge calculus, which is a discrete model for quantum gravity, appearing in the semi--classical limit of spin foam models. To this end we develop a technique to evaluate the linearized Regge action associated to Pachner moves in 3D and 4D and show that it has a simple, factorized structure. We succeed in finding a local measure for 3D (linearized) Regge calculus that leads to triangulation independence. This measure factor coincides with the asymptotics of the Ponzano Regge Model, a 3D spin foam model for gravity. We furthermore discuss to which extent one can find a triangulation independent measure for 4D Regge calculus and how such a measure would be related to a quantum model for 4D flat space. To this end, we also determine the dependence of classical Regge calculus on the choice of triangulation in 3D and 4D

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Section: Discussionmentioning

confidence: 99%

Path integral measure and triangulation independence in discrete gravity

2012

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“…Nevertheless, there is good evidence that the transition amplitudes for semiclassical states 29 are able to select dynamically the globally oriented configurations (see [51] for a comprehensive discussion in the context of Regge calculus and [57] for a single-vertex discussion in spinfoams). In the Lorentzian setting, the definition of causal amplitudes makes use of modified spinfoam amplitudes which are orientation-dependent [58][59][60].…”

Section: Discussionmentioning

confidence: 99%

“…This amounts to dropping one SL(2, C) integral per each vertex.The map Y is constructed using the principal series of unitary representations H (j,ρ) of SL(2, C), which are infinite dimensional and labeled by a half-integer j and a positive real number ρ. The spinfoam model imposes the constraint ρ = γk(59)…”

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confidence: 99%

Regge Gravity From Spinfoams

Magliaro

Perini

2013

Int. J. Mod. Phys. D

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We consider spinfoam quantum gravity for general triangulations in the regime l 2 P a a/γ, namely in the combined classical limit of large areas a and flipped limit of small Barbero-Immirzi parameter γ, where lP is the Planck length. Under few working hypotheses we find that the flipped limit enforces the constraints that turn the spinfoam theory into an effective Regge-like quantum theory with lengths as variables, while the classical limit selects among the possible geometries the ones satisfying the Einstein equations. Two kinds of quantum corrections appear in terms of powers of l 2 P /a and γl 2 P /a. The result also suggests that the Barbero-Immirzi parameter may run to smaller values under coarse-graining of the triangulation.

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“…Further investigation is still necessary to better understand the issue and how it is related to the imposition of constraints in the spin-foam path integral. We would however be remiss in not pointing out that the Cosine Problem's existence has been associated to a time-orientation symmetry in spin-foam models: in [52,53] the point is made that a causal ordering for spin-foams may be enforced by making the amplitudes explicitly dependent on the orientation of the geometry, thus breaking time reversal symmetry. As we have shown, spin-foam vertices with mixed causal characters induce a second solution if one transforms the boundary data appropriately.…”

Section: Discussion and Outlookmentioning

confidence: 99%

Asymptotic analysis of spin-foams with time-like faces in a new parameterisation

Simão,

Steinhaus

2021

Preprint

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In this article we study the Conrady-Hnybida extension of the Lorentzian Engle-Pereira-Rovelli-Livine spin-foam model, which admits time-like cells rather than just space-like ones. Our focus is on the asymptotic analysis of the model's vertex amplitude.We propose a new parameterisation for states associated to time-like 3-cells, from which we derive a closed-form expression for their amplitudes. This allows us to revisit the conditions under which critical points of the amplitudes occur, and we find Regge-like geometrical critical points in agreement with the literature. However, we find also evidence for non-geometrical points which are not dynamically suppressed without further assumptions; the model then does not strictly asymptote to the Regge action, contrary to what one would expect. We moreover prove Minkowski and rigidity theorems for Minkowskian polyhedra, extending the asymptotic analysis to non-simplicial spin-foams. Lastly, we present evidence that the so-called "Cosine Problem" is not present for 4-cells containing both space-and time-like 3-cells.

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The Feynman propagator for quantum gravity: spin foams, proper time, orientation, causality and timeless-ordering

Cited by 7 publications

References 16 publications

Path integral measure and triangulation independence in discrete gravity

Path integral measure and triangulation independence in discrete gravity

Regge Gravity From Spinfoams

Asymptotic analysis of spin-foams with time-like faces in a new parameterisation

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