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We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter.
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Barros e Sá N., Hamiltonian analysis of general relativity with the Immirzi parameter,
2001
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Alexandrov S., Livine E.R., SU(2) loop quantum gravity seen from covariant theory,
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Meissner K.A., Black-hole entropy in loop quantum gravity,
2004
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Agulló I., Barbero J.F., Díaz-Polo J., Fernández-Borja E., Villaseñor E.J.S., Black hole state counting in loop quantum gravity: a number-theoretical approach,
2008
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2008
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Freidel L., Krasnov K., A new spin foam model for 4D gravity,
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Samuel J., Is Barbero’s Hamiltonian formulation a gauge theory of Lorentzian gravity?,
2000
Cited alongside, same era.
Alexandrov S., Vassilevich D., Area spectrum in Lorentz-covariant loop gravity,
2001
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2008
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Geiller M., Lachièze-Rey M., Noui K., A new look at Lorentz-covariant loop quantum gravity,
2011
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Rovelli C., Speziale S., Lorentz covariance of loop quantum gravity,
2011
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