New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis

@article{Bodendorfer2013NewVF,
  title={New variables for classical and quantum gravity in all dimensions: I. Hamiltonian analysis},
  author={Norbert Bodendorfer and Thomas Thiemann and Andreas Thurn},
  journal={Classical and Quantum Gravity},
  year={2013},
  volume={30},
  pages={045001}
}
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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References

SHOWING 1-10 OF 73 REFERENCES
New Variables for Classical and Quantum Gravity in all Dimensions II. Lagrangian Analysis
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
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
Reduced phase space quantization and Dirac observables
In her recent work, Dittrich generalized Rovelli's idea of partial observables to construct Dirac observables for constrained systems to the general case of an arbitrary first class constraint
Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action.
  • Holst
  • Mathematics
    Physical review. D, Particles and fields
  • 1996
TLDR
Barbero’s Hamiltonian formulation is derived from an action, which can be considered as a generalization of the ordinary Hilbert-Palatini action, and provides a real theory of gravity with a connection as configuration variable, and with the usual Gauss and vector constraint.
SU(2) loop quantum gravity seen from covariant theory
Covariant loop gravity comes out of the canonical analysis of the Palatini action and the use of the Dirac brackets arising from dealing with the second class constraints (“simplicity” constraints).
Modern Canonical Quantum General Relativity
The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly
Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector
In our companion paper, we focused on the quantization of the Rarita–Schwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime
Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the
Uniqueness of Diffeomorphism Invariant States on Holonomy–Flux Algebras
Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:
...
1
2
3
4
5
...