# Spin foam model for Lorentzian general relativity

@article{Perez2001SpinFM, title={Spin foam model for Lorentzian general relativity}, author={Alejandro Perez and Carlo Rovelli}, journal={Physical Review D}, year={2001}, volume={63}, pages={041501} }

We present a spin foam formulation of Lorentzian quantum General Relativity. The theory is based on a simple generalization of an Euclidean model defined in terms of a field theory over a group. Its vertex amplitude turns out to be the one recently introduced by Barrett and Crane. As in the case of its Euclidean relatives, the model fully implements the desired sum over 2-complexes which encodes the local degrees of freedom of the theory.

## Figures from this paper

## 111 Citations

Timelike surfaces in Lorentz covariant loop gravity and spin foam models

- Physics
- 2005

We apply a recently developed canonical formulation of general relativity, which possesses explicit covariance with respect to Lorentz transformations in the tangent space, to describe the case of a…

Cosmological deformation of Lorentzian spin foam models

- Physics
- 2003

We study the quantum deformation of the Barrett–Crane Lorentzian spin foam model which is conjectured to be the discretization of the Lorentzian Plebanski model with positive cosmological constant…

Cosmological deformation of Lorentzian spin foam models

- Physics
- 2003

We study the quantum deformation of the Barrett?Crane Lorentzian spin foam model which is conjectured to be the discretization of the Lorentzian Plebanski model with positive cosmological constant…

A Finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity

- Physics, Mathematics
- 2001

We show that the normalized Lorentzian state sum is finite on any triangulation. It thus provides a candidate for a perturbatively finite quantum theory of general relativity in four dimensions with…

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,…

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…

Regularization and finiteness of the Lorentzian loop quantum gravity vertices

- Mathematics
- 2009

We give an explicit form for the Lorentzian vertices recently introduced for possibly defining the dynamics of loop quantum gravity. As a result of doing so, a natural regularization of the vertices…

Finiteness and dual variables for Lorentzian spin foam models

- Mathematics
- 2006

We describe here some new results concerning the Lorentzian Barrett–Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a…

Construction of the General Spin Foam Model of Lorentzian BF theory and Gravity

- Mathematics
- 2003

In this article we report our progress in the construction of a general Lorentzian spin foam model based on the Gelfand-Năımark theory of the representations of SL(2, C) which might include both…

## References

SHOWING 1-10 OF 23 REFERENCES

Canonical “Loop” Quantum Gravity and Spin Foam Models

- Physics
- 1999

The canonical “loop” formulation of quantum gravity is a mathematically well defined, background independent, non-perturbative standard quantization of Einstein’s theory of General Relativity. Some…

Spacetime as a Feynman diagram: the connection formulation

- Physics
- 2001

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…

The Lorentz Group and the Sphere

- Mathematics
- 1970

A direct connection between the spin and conformally weighted functions on the sphere and geometric objects in Minkowski space is established through the isomorphism of the conformal group of the…

A lattice quantum gravity model with surface-like excitations in 4-dimensional spacetime

- Physics
- 2000

A lattice quantum gravity model in 4 dimensional Riemannian spacetime is constructed based on the SU(2) Ashtekar formulation of general relativity. This model can be understood as one of the family…

'Sum over surfaces' form of loop quantum gravity

- Physics
- 1997

We derive a spacetime formulation of quantum general relativity from (hamiltonian) loop quantum gravity. In particular, we study the quantum propagator that evolves the 3-geometry in proper time. We…

A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces

- Physics
- 1994

We show that the partition function of the Ponzano-Regge quantum gravity model can be written as a sum over surfaces in a $(2+1)$ dimensional space-time. We suggest a geometrical meaning, in terms of…

Relativistic spin networks and quantum gravity

- Physics
- 1998

Relativistic spin networks are defined by considering the spin covering of the group SO(4), SU(2)×SU(2). Relativistic quantum spins are related to the geometry of the two-dimensional faces of a…