Functional integration on two-dimensional Regge geometries

Menotti, Pietro; Peirano, Pier Paolo

doi:10.1016/0550-3213(96)00260-x

Cited by 25 publications

(22 citation statements)

References 25 publications

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“…Perturbatively, one can study expectation values of products of localized operators, such as the correlation of volumes of two tetrahedra belonging to 13 For an analysis in two dimensions see [87] and [88,89,90,91]. 14 See for instance [72], [73] and references therein.…”

Section: Correlations In Perturbative Quantum Regge-calculusmentioning

confidence: 99%

The perturbative Regge-calculus regime of loop quantum gravity

Bianchi

Modesto²

2008

Nuclear Physics B

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The relation between Loop Quantum Gravity and Regge calculus has been pointed out many times in the literature. In particular the large spin asymptotics of the Barrett-Crane vertex amplitude is known to be related to the Regge action. In this paper we study a semiclassical regime of Loop Quantum Gravity and show that it admits an effective description in terms of perturbative area-Regge-calculus. The regime of interest is identified by a class of states given by superpositions of four-valent spin networks, peaked on large spins.As a probe of the dynamics in this regime, we compute explicitly two-and three-area correlation functions at the vertex amplitude level. We find that they match with the ones computed perturbatively in area-Regge-calculus with a single 4-simplex, once a specific perturbative action and measure have been chosen in the Regge-calculus path integral. Correlations of other geometric operators and the existence of this regime for other models for the dynamics are briefly discussed.

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Section: Correlations In Perturbative Quantum Regge-calculusmentioning

confidence: 99%

The perturbative Regge-calculus regime of loop quantum gravity

Bianchi

Modesto²

2008

Nuclear Physics B

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“…In the limit ε → 0 the summation over this grid reproduces the continuum result (6). An alternative and conceptually quite nice approach was studied in [4]. In these papers the continuum functional integral over all metrics is replaced by the continuum functional integral over so-called piecewise linear metrics, i.e.…”

Section: Introductionmentioning

confidence: 99%

Spikes in quantum Regge calculus

Ambjørn¹,

Nielsen²,

Rolf³

et al. 1997

Class. Quantum Grav.

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We demonstrate by explicit calculation of the DeWitt-like measure in two-dimensional quantum Regge gravity that it is highly non-local and that the average values of link lengths l, < l n >, do not exist for sufficient high powers of n. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This might explain the failure of quantum Regge calculus to reproduce the continuum results of two-dimensional quantum gravity. It points to severe problems for the Regge approach in higher dimensions.

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“…Some results in such a direction have been recently discussed by Catterall and Mottola with an emphasis on the numerical simulation, [6]. Menotti and Peirano [7] discussed a similar issue in connection with the Regge measure in simplicial quantum gravity. However in such a case the problem takes on a rather different flavor, being more directly connected with the issue of the diffeomorphism invariance of the resulting measure.…”

Section: Introductionmentioning

confidence: 94%

Conformal modes in simplicial quantum gravity and the Weil–Petersson volume of moduli space

Carfora¹,

Marzuoli²

2002

Advances in Theoretical and Mathematical Physics

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Our goal here is to present a detailed analysis connecting the anomalous scaling properties of 2D simplicial quantum gravity to the geometry of the moduli space M g , N0 of genus g Riemann surfaces with N 0 punctures. In the case of pure gravity we prove that the scaling properties of the set of dynamical triangulations with N 0 vertices are directly provided by the large N 0 asymptotics of the Weil-Petersson volume of M g , N0 , recently discussed by Manin and Zograf. Such a geometrical characterization explains why dynamical triangulations automatically take into account the anomalous scaling properties of Liouville theory. In the case of coupling with conformal matter we briefly argue that the anomalous scaling of the resulting discretized theory should be related to the Gromov-Witten invariants of the moduli space M g , N0 (X, β) of stable maps from (punctured Riemann surfaces associated with) dynamical triangulations to a (smooth projective) manifold X parameterizing the conformal matter configurations. e-print archive: http://lanl.arXiv.org/abs/math-ph/0107028

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Functional integration on two-dimensional Regge geometries

Cited by 25 publications

References 25 publications

The perturbative Regge-calculus regime of loop quantum gravity

The perturbative Regge-calculus regime of loop quantum gravity

Spikes in quantum Regge calculus

Conformal modes in simplicial quantum gravity and the Weil–Petersson volume of moduli space

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