New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis

@article{Bodendorfer2011NewVF,
  title={New variables for classical and quantum gravity in all dimensions: II. Lagrangian analysis},
  author={Norbert Bodendorfer and Thomas Thiemann and A. Thurn},
  journal={Classical and Quantum Gravity},
  year={2011},
  volume={30}
}
We rederive the results of our companion paper, for matching space–time and internal signature, by applying in detail the Dirac algorithm to the Palatini action. While the constraint set of the Palatini action contains second class constraints, by an appeal to the method of gauge unfixing, we map the second class system to an equivalent first class system which turns out to be identical to the first class constraint system obtained via the extension of the ADM phase space performed in our… 
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In this paper, we discuss several approaches to solve the quadratic and linear simplicity constraints in the context of the canonical formulations of higher dimensional general relativity and
New variables for classical and quantum gravity in all dimensions: IV. Matter coupling
We employ the techniques introduced in the companion papers (Bodendorfer et al 2011 arXiv:1105.3703 [gr-qc]; arXiv:1105.3704 [gr-qc]; arXiv:1105.3705 [gr-qc]) to derive a connection formulation of
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