New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory

@article{Bodendorfer2011NewVF,
  title={New Variables for Classical and Quantum Gravity in all Dimensions III. Quantum Theory},
  author={Norbert Bodendorfer and Thomas Thiemann and Andreas Thurn},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2011}
}
We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalise to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its "diagonal" components acting at edges of spin network functions are easily solved, its "off-diagonal" components acting at vertices are non trivial… 
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