A new look at Lorentz-Covariant Loop Quantum Gravity

@article{Geiller2011ANL,
  title={A new look at Lorentz-Covariant Loop Quantum Gravity},
  author={Marc Geiller and Marc Lachi{\`e}ze‐Rey and Karim Noui},
  journal={Physical Review D},
  year={2011},
  volume={84},
  pages={044002}
}
In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the canonical analysis of the Holst action without the time-gauge. We show that it has the property of lying in the conjugacy class of a pure $\su(2)$ connection, a result which enables one to construct the kinematical Hilbert space of the Lorentz-covariant theory in… 
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