The quantization of Regge calculus

Roček, Martin; Williams, Ruth M.

doi:10.1007/bf01581603

Cited by 167 publications

(185 citation statements)

References 6 publications

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“…However the implementation of a meaningful analogue of this procedure (and even the existence of one) in a general-boundary setting is still unclear 17 . A more promising route might be to select the boundary state representing the semiclassical regime in an a posteriori way, by requiring that the results match those of conventional perturbative Regge theory (in which only small fluctuations around a given classical solution for the whole manifold are quantized and summed over; see [60,61,62]). Clearly this vindicates the general Gaussian expression to the lowest order, and the free parameters α ij in this parametrization (one for each pair of boundary edges L i , L j ) can be established a posteriori by matching the correlations between each pair of boundary edges with the conventional perturbative expression for it.…”

Section: Discussionmentioning

confidence: 99%

Semiclassical regime of Regge calculus and spin foams

Bianchi

Satz

2009

Nuclear Physics B

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Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine -as expected from the semiclassical limit of spin foam models -then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.

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Section: Discussionmentioning

confidence: 99%

Semiclassical regime of Regge calculus and spin foams

Bianchi

Satz

2009

Nuclear Physics B

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“…Although Regge worked in a context which was purely classical, later Wheeler [Wh] speculated on the possibility of employing Regge calculus as a tool for constructing a quantum theory of gravity (see also [CMS1,Fro,H,HP,HS,L2,MTW,PR,RW1,RW2,Wei,Wa]). This approach is in some respects similar to the use of lattice approximations in gauge theories, and thus might also be useful for numerical calculations (for further discussions of Regge calculus in the classical context, see [CW1,CW3,LI,WE,Wo]).…”

Section: T N~j Xmj T"-j*dmjmentioning

confidence: 99%

On the curvature of piecewise flat spaces

Müller²,

1984

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Abstract. We consider analogs of the Lipschitz-Killing curvatures of smooth Riemannian manifolds for piecewise flat spaces. In the special case of scalar curvature, the definition is due to T. Regge considerations in this spirit date back to J. Steiner. We show that if a piecewise flat space approximates a smooth space in a suitable sense, then the corresponding curvatures are close in the sense of measures.

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“…For gravity, this concept is intertwined with the appearance of discrete representation of diffeomorphism symmetry in the lattice models [36][37][38][39][40][41]. Such a discrete notion of diffeomorphism symmetry can arise in the form of vertex translations [42][43][44][45][46]. Discrete geometries can be represented by a triangulation carrying geometric data, for instance, in the Regge calculus [47,48], the lengths of the edges in the triangulation.…”

Section: Introductionmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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The quantization of Regge calculus

Cited by 167 publications

References 6 publications

Semiclassical regime of Regge calculus and spin foams

Semiclassical regime of Regge calculus and spin foams

On the curvature of piecewise flat spaces

Spin Foam Models with Finite Groups

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