A new spin foam model for 4D gravity
@article{Freidel2007ANS, title={A new spin foam model for 4D gravity}, author={Laurent Freidel and Kirill Krasnov}, journal={Classical and Quantum Gravity}, year={2007}, volume={25}, pages={125018} }
Starting from Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4D Riemannian quantum gravity that generalizes the well-known Barrett–Crane model and resolves the inherent to it ultra-locality problem. The BF formulation of 4D gravity possesses two sectors: gravitational and topological ones. The model presented here is shown to give a quantization of the gravitational sector, and is dual to the recently proposed spin foam model of Engle et al…
475 Citations
Spin foam model from canonical quantization
- Physics
- 2008
We suggest a modification of the Barrett-Crane spin foam model of four-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop…
Spin foam models and the Duflo map
- Biology
- 2018
A new spin foam model for 4d quantum gravity is constructed, using the flux representation of states and amplitudes, based on the Duflo quantization map and the associated non-commutative Fourier transform for Lie groups.
Spin Foams and Canonical Quantization
- Physics
- 2012
This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions. In the three-dimensional context, where the…
Effective Spin Foam Models for Four-Dimensional Quantum Gravity.
- PhysicsPhysical review letters
- 2020
This work introduces a family of "effective" spin foam models that incorporate a quantum area spectrum, impose gluing constraints as strongly as possible, and leverage the discrete general relativity action to specify amplitudes.
Effective spin foam models for Lorentzian quantum gravity
- Physics
- 2021
Making the Lorentzian path integral for quantum gravity well-defined and computable has been a long standing challenge. In this work we adopt the recently proposed effective spin foam models to the…
The physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory
- Physics
- 2010
A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we…
Holonomy Spin Foam Models: Definition and Coarse Graining
- Physics
- 2013
We propose a new holonomy formulation for spin foams, which naturally extends the theory space of lattice gauge theories. This allows current spin foam models to be defined on arbitrary 2-complexes…
Classical GR as a topological theory with linear constraints
- Physics
- 2011
We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type…
Towards vertex renormalization in 4d Spin Foams
- Physics
- 2017
A long-standing open problem in 4-dimensional Spin Foam models of Quantum Gravity has been the behavior of the amplitudes under coarse graining. In this thesis, we attempt to study this question by…
References
SHOWING 1-10 OF 37 REFERENCES
Spin foam model from canonical quantization
- Physics
- 2008
We suggest a modification of the Barrett-Crane spin foam model of four-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop…
so(4) Plebanski action and relativistic spin-foam model
- Physics
- 1998
We study the correspondence between the `relativistic spin-foam' model introduced by Barrett, Crane and Baez and the so(4) Plebanski action. We argue that the so(4) Plebanski model is the continuum…
Spin Foam Models and the Classical Action Principle
- Physics
- 1998
We propose a new systematic approach that allows one to derive the spin foam (state sum) model of a theory starting from the corresponding classical action functional. It can be applied to any theory…
Simplicity and closure constraints in spin foam models of gravity
- Physics
- 2008
We revise the imposition of various constraints in spin foam models of four-dimensional general relativity. We argue that the usual simplicity constraint must be supplemented by a constraint on…
3+1 spinfoam model of quantum gravity with spacelike and timelike components
- Mathematics
- 2000
We present a spin foam formulation of Lorentzian quantum general relativity. The theory is based on a simple generalization of a Euclidean model defined in terms of a field theory over a group. The…
Hidden quantum gravity in 3D Feynman diagrams
- Physics
- 2006
In this work we show that 3D Feynman amplitudes of standard quantum field theory in flat and homogeneous space can be naturally expressed as expectation values of a specific topological spin foam…
Barrett-Crane spin foam model from generalized BF-type action for gravity
- Physics
- 2002
We study a generalized action for gravity as a constrained BF theory, and its relationship with the Plebanski action. We analyse the discretization of the constraints and the spin foam quantization…
BF Description of Higher-Dimensional Gravity Theories
- Physics
- 1999
It is well known that, in the first-order formalism, pure three-dimensional gravity is just the BF theory. Similarly, four-dimensional general relativity can be formulated as BF theory with an…
A Lorentzian signature model for quantum general relativity
- Mathematics, Physics
- 2000
We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra.
We propose a combinatorial model for the path integral…