LQG propagator from the new spin foams

Bianchi, Eugenio; Magliaro, Elena; Perini, Claudio

doi:10.1016/j.nuclphysb.2009.07.016

Cited by 105 publications

(196 citation statements)

References 50 publications

Supporting

Mentioning

183

Contrasting

Order By: Relevance

“…When the simplicial triangulation is refined, given a Regge geometry {ℓ} which approximate a smooth geometry 13 , the 13 If we embed the Regge geometry in R N , N > 4, the corresponding smooth geometry is an smooth enveloping surface S of the Regge geometry, where all vertices (end points of ℓ's) in the Regge geometry are located in S . S is required to satisfy ρ ≫ ℓ everywhere.…”

Section: The Essential Contribution Of the Spinfoam Amplitudementioning

confidence: 99%

See 1 more Smart Citation

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Han

2017

Phys. Rev. D

View full text Add to dashboard Cite

In this paper we explain how 4-dimensional general relativity and in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit which couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of Einstein equation can be approached by dominant configurations in spinfoam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spinfoam formulation, and how to take advantage of it.

show abstract

Section: The Essential Contribution Of the Spinfoam Amplitudementioning

confidence: 99%

“…This proposal produces Regge equation (equation of motion from Regge action) from spinfoam amplitude. The idea of this type of limit has also been used in the graviton propagator computation from spinfoams [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Han

2017

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…For the given graph γ in figure 14, there is only one such spin foam, and its one vertex is dual (in four dimensions) to a single 4-simplex, of which γ forms the boundary. The quantity (33) has been calculated in [52,53] (to leading order in λ). It has been found to match, at least in part, the same result one would calculate in a more classic, but incomplete quantum gravity framework -linearized quantum gravity [54,55,51] -the beginnings of which date back to the work of Rosenfeld, Fierz and Pauli in the 1930's [2].…”

Section: The Calculationmentioning

confidence: 99%

Spin Foams

Engle¹

2014

Springer Handbook of Spacetime

View full text Add to dashboard Cite

Ever since special relativity, space and time have become seamlessly merged into a single entity, and space-time symmetries, such as Lorentz invariance, have played a key role in our fundamental understanding of nature. Quantum mechanics, however, did not originally conform to this new way of thinking. The original formulation of quantum mechanics, called 'canonical', involves wavefunctions, operators, Hamiltonians, and time evolution in a way that treats time very differently from space. This situation was improved by Feynman, who formulated quantum mechanics in terms of probabilities calculated by summing over amplitudes associated to classical histories -the path integral formulation of quantum mechanics. As histories are naturally space-time objects in which space and time can be viewed 'on equal footing', the path integral formulation allowed, for the first time, space-time symmetries to be manifest in a general quantum theory.The key insight of Einstein's theory of gravity, general relativity, is that gravity is spacetime geometry. Space-time geometry, the one 'background structure' -i.e., non-dynamical space-time structure -remaining after special relativity, was discovered to be dynamical and to describe the gravitational field, revealing nature to be 'background independent.' Background independence can equivalently be expressed in terms of a profound enlargement of the basic spacetime symmetry group of physics: invariance under Lorentz transformations and translations is replaced by invariance under the much larger group of space-time diffeomorphisms.We have already seen in the chapter by Sahlmann on gravity, geometry and the quantum, a canonical quantization of Einstein's gravity, and hence of geometry, in which geometric operators are derived with discrete eigenvalues [1, 2, 3]. Instead of space being a smooth continuum, we see that it comes in discrete quanta -minimal 'chunks of space.' Furthermore, as discussed in the chapter by Agullo and Corichi, when applied to cosmology, this quantum theory of gravity leads to a new understanding of the Big Bang in which usually problematic infinities are resolved, and one can actually ask what happened before the Big Bang. In spite of these successes, because it is a canonical theory, it has as a drawback that space-time symmetries, in particular space-time diffeomorphism symmetry, are not manifest. Equivalently, the preferred separation between space and time prevents full background independence from being manifest.One can ask: Is there a way to construct a path-integral formulation of quantum gravity, in which the most radical discovery of general relativity, background independence, or equivalently, space-time diffeomorphism invariance, can be fully manifest, which nevertheless retains the successes of the canonical theory? This is the question leading to the spin foam program. In answering it one must understand more carefully the relationship between the canonical and path integral formulations of quantum mechanics, and in particular how these apply to g...

show abstract

“…The large-spin asymptotics of the correlation function (13) can be obtained via stationary phase approximation [3,6], which is given by (for details, see [4]): …”

Section: The Eprl Correlation Functionsmentioning

confidence: 99%

“…If we take the classical limit, introduced in [3], where the Barbero-Immirzi parameter is taken to zero γ → 0, and the spin of the boundary state is taken to infinity j → ∞, keeping the size of the quantum geometry A ∼ γj finite and fixed, the two-point function (16) we obtain exactly matches the one obtained from Lorentzian Regge calculus [9]. Deriving the LQG correlation function at the level of a single spin foam vertex is certainly only a first step.…”

Section: The Eprl Correlation Functionsmentioning

confidence: 99%