# Loop-quantum-gravity vertex amplitude.

@article{Engle2007LoopquantumgravityVA, title={Loop-quantum-gravity vertex amplitude.}, author={J S Engle and Roberto Pereira and Carlo Rovelli}, journal={Physical review letters}, year={2007}, volume={99 16}, pages={ 161301 } }

Spin foam models are hoped to provide the dynamics of loop-quantum gravity. However, the most popular of these, the Barrett-Crane model, does not have the good boundary state space and there are indications that it fails to yield good low-energy n-point functions. We present an alternative dynamics that can be derived as a quantization of a Regge discretization of Euclidean general relativity, where second class constraints are imposed weakly. Its state space matches the SO(3) loop gravity one…

## 283 Citations

Lorentzian loop quantum gravity vertex amplitude

- Physics
- 2008

We generalize a model recently proposed for Euclidean quantum gravity to the case of Lorentzian signature. The main features of the Euclidean model are preserved in the Lorentzian one. In particular,…

Linking covariant and canonical loop quantum gravity: New solutions to the Euclidean scalar constraint

- Physics
- 2012

It is often emphasized that spin-foam models could realize a projection on the physical Hilbert space of canonical Loop Quantum Gravity (LQG). As a first test we analyze the one-vertex expansion of a…

A new look at loop quantum gravity

- Physics
- 2010

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined…

The volume operator in covariant quantum gravity

- Physics
- 2010

A covariant spin-foam formulation of quantum gravity has recently been developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular,…

Loop Quantum Gravity

- Physics
- 2014

This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of…

Spin foam models: the dynamics of quantum geometry

- Physics
- 2008

In this paper, we give an overview of the main techniques developed in the context of background independent gravity in order to tackle the problem of the dynamics. We briefly introduce loop quantum…

Loop quantum gravity - a short review

- Physics
- 2010

In this article we review the foundations and the present status of loop quantum gravity. It is short and relatively non-technical, the emphasis is on the ideas, and the flavor of the techniques. In…

Second-order amplitudes in loop quantum gravity

- Physics
- 2009

We explore some second-order amplitudes in loop quantum gravity. In particular, we compute some second-order contributions to diagonal components of the graviton propagator in the large distance…

## References

SHOWING 1-10 OF 51 REFERENCES

Three-dimensional loop quantum gravity: physical scalar product and spin-foam models

- Physics
- 2005

In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection…

New spinfoam vertex for quantum gravity

- Physics
- 2007

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the…

Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

- Physics
- 2001

This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity,…

On choice of connection in loop quantum gravity

- Physics
- 2001

We investigate the quantum area operator in the loop approach based on the Lorentz covariant Hamiltonian formulation of general relativity. We show that there exists a two-parameter family of Lorentz…

Weaving a classical metric with quantum threads.

- PhysicsPhysical review letters
- 1992

It is shown that there exist quantum states which approximate a given metric at large scales, but such states exhibit a discrete structure at the Planck scale.

Quantum Spin Dynamics (QSD)

- Physics
- 1998

An anomaly-free operator corresponding to the Wheeler - DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is…

Graviton propagator from background-independent quantum gravity.

- PhysicsPhysical review letters
- 2006

A component of the propagator is computed to first order, under some approximations, obtaining the correct large-distance behavior, indicating a way for deriving conventional spacetime quantities from a background-independent theory.

An Introduction to spin foam models of quantum gravity and BF theory

- Physics
- 1999

In loop quantum gravity we now have a clear picture of the quantum geometry of space, thanks in part to the theory of spin networks. The concept of ‘spin foam’ is intended to serve as a similar…

SU(2) loop quantum gravity seen from covariant theory

- Physics
- 2003

Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints).…

Knot theory and quantum gravity.

- MathematicsPhysical review letters
- 1988

A new represenatation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in three-space. In this representation exact solutions of the quantum…