Spin networks for noncompact groups

@article{Freidel2003SpinNF,
  title={Spin networks for noncompact groups},
  author={Laurent Freidel and Etera R. Livine},
  journal={Journal of Mathematical Physics},
  year={2003},
  volume={44},
  pages={1322-1356}
}
Spin networks are a natural generalization of Wilson loop functionals. They have been extensively studied in the case where the gauge group is compact and it has been shown that they naturally form a basis of gauge invariant observables. Physically the restriction to compact gauge groups is enough for the study of Yang–Mills theories, however it is well known that noncompact groups naturally arise as internal gauge groups for Lorentzian gravity models. In this context, a proper construction of… 
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References

SHOWING 1-10 OF 44 REFERENCES
Spin Networks in Nonperturbative Quantum Gravity
A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objects
Representation Theory of Analytic Holonomy C* Algebras
Integral calculus on the space of gauge equivalent connections is developed. Loops, knots, links and graphs feature prominently in this description. The framework is well--suited for quantization of
Quantum theory of geometry: I. Area operators
A new functional calculus, developed recently for a fully non-perturbative treatment of quantum gravity, is used to begin a systematic construction of a quantum theory of geometry. Regulated
Spin networks and quantum gravity.
  • Rovelli, Smolin
  • Physics
    Physical review. D, Particles and fields
  • 1995
TLDR
A new basis on the state space of non-perturbative quantum gravity is introduced that allows a simple expression for the exact solutions of the Hamiltonian constraint (Wheeler-DeWitt equation) that have been discovered in the loop representation.
Quantum Spin Dynamics (QSD)
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
A Lorentzian signature model for quantum general relativity
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
Loop representations for (2+1) gravity on a torus
We study the loop representation of the quantum theory for 2+1-dimensional general relativity on a manifold M=T2*R, where T2 is the torus, and compare it with the connection representation for this
Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$ and $SU(1,1)$-connections
The structure of the moduli spaces M:=A/G of (all, not just flat) SL(2,C) and SU(1,1) connections on an n-manifold is analysed. For any topology of the corresponding spaces A of all connections which
...
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