A Lorentzian signature model for quantum general relativity

@article{Barrett2000ALS,
  title={A Lorentzian signature model for quantum general relativity},
  author={John W. Barrett and Louis Crane},
  journal={Classical and Quantum Gravity},
  year={2000},
  volume={17},
  pages={3101-3118}
}
  • J. Barrett, L. Crane
  • Published 9 April 1999
  • Mathematics, Physics
  • Classical and Quantum Gravity
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 given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are… 
View PDF on arXiv
317 Citations
Highly Influential Citations
21
Background Citations
99
Methods Citations
74
Results Citations
6

317 Citations

Citation Type

Citation Type

Spin foam model for Lorentzian general relativity
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…
Cosmological deformation of Lorentzian spin foam models
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…
Quantum Gravity as a Deformed Topological Quantum Field Theory
It is known that the Einstein-Hilbert action with a positive cosmological constant can be represented as a perturbation of the SO(4, 1) BF theory by a symmetry-breaking term quadratic in the B field.…
Lorentzian loop quantum gravity vertex amplitude
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,…
Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity
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,…
3+1 spinfoam model of quantum gravity with spacelike and timelike components
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…
Lorentzian LQG vertex amplitude
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,…
Integrability for relativistic spin networks
The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph…
4-dimensional Spin-foam Model with Quantum Lorentz Group
We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model…
Simple model for quantum general relativity from loop quantum gravity
New progress in loop gravity has lead to a simple model of ‘general-covariant quantum field theory’. I sum up the definition of the model in self-contained form, in terms accessible to those outside…
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 66 REFERENCES
Relativistic spin networks and quantum gravity
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…
An Introduction to spin foam models of quantum gravity and BF theory
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…
Harmonic Analysis on the quantum Lorentz group
This work begins with a review of complexification and realification of Hopf algebras. We emphasize the notion of multiplier Hopf algebras for the description of different classes of functions…
'Sum over surfaces' form of loop quantum gravity
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…
Quantum models of space-time based on recoupling theory
Models of geometry that are intrinsically quantum-mechanical in nature arise from the recoupling theory of space-time symmetry groups. Roger Penrose constructed such a model from SU(2) recoupling in…
Harmonic Analysis on the Quantum Lorentz Group
Abstract:Using a continuation of 6j symbols of SUq(2) with complex spins, we give a new description of the unitary representations of SLq(2 ℂ)ℝ and find explicit expressions for the characters of…
On relativistic spin network vertices
Barrett and Crane have proposed a model of simplicial Euclidean quantum gravity in which a central role is played by a class of Spin(4) spin networks called “relativistic spin networks” which satisfy…
Knots and quantum gravity: Progress and prospects
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and…
Quantum deformations of the Lorentz group
Three properties characteristic for the Lorentz group are selected and all quantum groups with the same properties are found. As a result, a number of one, two and three parameter quantum…
(2+1)-Dimensional Gravity as an Exactly Soluble System
...
1
2
3
4
5
...