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Testing the role of the Barbero-Immirzi parameter and the choice of connection in loop quantum gravity
We study the role of the Barbero-Immirzi parameter $\ensuremath{\gamma}$ and the choice of connection in the construction of (a symmetry-reduced version of) loop quantum gravity. We start with the four-dimensional Lorentzian Holst action that we reduce to three dimensions in a way that preserves the presence of $\ensuremath{\gamma}$. In the …