Spacetime as a Feynman diagram: the connection formulation

By Michael P Reisenberger, Carlo Rovelli. 2000

239 citations recorded by the source corpus.

Spin-foam models are the path-integral counterparts to loop-quantized canonical theories. Over 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 accommodate 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 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. 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: here we present a new and more detailed derivation based on the connection formulation of the spin-foam models.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7c3c2bacb89ccdb9aee245201b77957d4d021cfc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Group Field Theory: An Overview (2005, background): “[13] M. P. Reisenberger and C. Rovelli, “*Sum over surfaces* form of loop quantum gravity,” Phys.”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, background): “Boundary states of the theory assume the form of spin networks, and the Feynman amplitudes assume the form of spin foammodels [30] (TGFTs become then a natural way to remove the dependence of the spin foam dynamics from a given cellular complex).”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “The fundamental observation is that spin foams admit a dual formulation in terms of a field theory over a group manifold [133, 315, 314].”
Homogeneous cosmologies as group field theory condensates (2013, background): “In fact, spin foam models and group field theories are in one-to-one correspondence [30].”
Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory (2005, background): “An interesting perspective appear if one remark that the structure of the effective field theory which arise here possess some strong similarity with the Group field theories that appears in the spin foam quantization of gravity [30], it is tempting to conjecture that this similarity is not purely a”
Zakopane lectures on loop gravity (2011, background): “Historically, spinfoams first appeared in LQG in this form, as histories of spin networks [26, 27, 28, 29, 30].”
Loop Quantum Gravity (2003, background): “It was later shown that any spin-foam model can be written as a group field theory [237, 238].”
LQG vertex with finite Immirzi parameter (2007, background): “It was shown in [16] that any spinfoam model [17], as the one we define here, admits a group field theory (GFT) [18] formulation, which is triangulation independent.”
Introduction to loop quantum gravity and spin foams (2004, background): “troduces the phase space functional K¯ := Z Σ Ki aE a i , (131) then the following series of identities hold: Ki a = γ −1(Ai a −Γ i a ) = 1 κγ Ai a,K¯ , (132) 38 Alejandro Perez K¯ = 1 γ3/2 SE(1),V , (133) where V = R p det(E) is the volume of Σ, and ﬁnally Eb i E c p j det(E) ǫijkǫ abc = 4 κγ Ak a,”