Causality in spin foam models

Gupta, Sameer

doi:10.1103/physrevd.61.064014

Cited by 8 publications

(17 citation statements)

References 26 publications

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“…• It realises the general definition given in [66] for a causal spin foam model (it is, to the best of our knowledge, its first non-trivial example), except for the use of the full Lorentz group instead of its SU (2) subgroup; its boundary states are thus covariant (simple) spin networks and it can be regarded as giving a path integral definition of the Hamiltonian constraint in covariant loop quantum gravity.…”

Section: A Causal Transition Amplitudementioning

confidence: 99%

Implementing causality in the spin foam quantum geometry

2003

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We analyse the classical and quantum geometry of the Barrett-Crane spin foam model for four dimensional quantum gravity, explaining why it has to be considering as a covariant realization of the projector operator onto physical quantum gravity states. We discuss how causality requirements can be consistently implemented in this framework, and construct causal transiton amplitudes between quantum gravity states, i.e. realising in the spin foam context the Feynman propagator between states. The resulting causal spin foam model can be seen as a path integral quantization of Lorentzian first order Regge calculus, and represents a link between several approaches to quantum gravity as canonical loop quantum gravity, sum-over-histories formulations, dynamical triangulations and causal sets. In particular, we show how the resulting model can be rephrased within the framework of quantum causal sets (or histories).2

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Section: A Causal Transition Amplitudementioning

confidence: 99%

Implementing causality in the spin foam quantum geometry

2003

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“…Fortunately, there are now non-trivial proposals [31,32,33,34,35,36,37] and results [38,39] concerning formulations of quantum gravity in terms of causal,lorentzian path integrals. In such a causal histories formulation, each history in the sum over histories comes with its own causal structure.…”

Section: Second Problem: Measurabilitymentioning

confidence: 99%

The strong and weak holographic principles

Smolin

2001

Nuclear Physics B

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We review the different proposals which have so far been made for the holographic principle and the related entropy bounds and classify them into the strong, null and weak forms. These are analyzed, with the aim of discovering which may hold at the level of the full quantum theory of gravity. We find that only the weak forms, which constrain the information available to observers on boundaries, are implied by arguments using the generalized second law. The strong forms, which go further and posit a bound on the entropy in spacelike regions bounded by surfaces, are found to suffer from serious problems, which give rise to counterexamples already at the semiclassical level. The null form, proposed by Fischler, Susskind, Bousso and others, in which the bound is on the entropy of certain null surfaces, appears adequate at the level of a bound on the entropy of matter in a single background spacetime, but attempts to include the gravitational degrees of freedom encounter serious difficulties. Only the weak form seems capable of holding in the full quantum theory.The conclusion is that the holographic principle is not a relationship between two independent sets of concepts: bulk theories and measures of geometry vrs boundary theories and measures of information. Instead, it is the assertion that in a fundamental theory the first set of concepts must be completely reduced to the second. * smolin@phys.psu.edu 1

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“…It is an old dream of gravity theorists to make topology dynamical, thus removing yet another element of a priori background structure. It would be interesting to sum even models formulated on a continous spacetime manifold, such as those found in [5,8] and [30], over spacetime topologies.…”

Section: Introductionmentioning

confidence: 99%

“…Of the spin foam models of gravity referred to above all but [5] and [30] are simplicial lattice models. A shortcoming of such models is that their predictions depend on the simplicial complex chosen to represent spacetime.…”

Section: Introductionmentioning

confidence: 99%

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Spacetime as a Feynman diagram: the connection formulation

Reisenberger

Rovelli

2000

Class. Quantum Grav.

172

262

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Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice truncates the presumably infinite set of gravitational degrees of freedom down to a finite set. Models that can accomodate an infinite set of degrees of freedom and that are independent of any background simplicial structure, or indeed any a priori spacetime topology, can be obtained from the lattice models by summing them over all lattice spacetimes. Here we show that this sum can be realized as the sum over Feynman diagrams of a quantum 1 field theory living on a suitable group manifold, with each Feynman diagram defining a particular lattice spacetime. We give an explicit formula for the action of the field theory corresponding to any given spin foam model in a wide class which includes several gravity models. Such a field theory was recently found for a particular gravity model [1]. Our work generalizes this result as well as Boulatov's and Ooguri's models of three and four dimensional topological field theories, and ultimately the old matrix models of two dimensional systems with dynamical topology. A first version of our result has appeared in a companion paper [2]: here we present a new and more detailed derivation based on the connection formulation of the spin foam models.

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Causality in spin foam models

Cited by 8 publications

References 26 publications

Implementing causality in the spin foam quantum geometry

Implementing causality in the spin foam quantum geometry

The strong and weak holographic principles

Spacetime as a Feynman diagram: the connection formulation

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