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 Andreas Thurn},
  journal={arXiv: General Relativity and Quantum Cosmology},
  year={2011}
}
We rederive the results of our companion paper, for matching spacetime 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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On the role of the Barbero-Immirzi parameter in discrete quantum gravity
The one-parameter family of transformations identified by Barbero and Immirzi plays a significant role in non-perturbative approaches to quantum gravity, among them loop quantum gravity and spin
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References

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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
On the Implementation of the Canonical Quantum Simplicity Constraint
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 [1, 2, 3] to derive a connection formulation of Lorentzian General Relativity coupled to Dirac fermions in dimensions D + 1 ≥ 3 with
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In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is
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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
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