This article is cited in 2 papers

Lorentz-Covariant Loop Quantum Gravity

S. Yu. Alexandrov

Utrecht University, Spinoza Institute

Abstract: We review the Lorentz-covariant approach to loop quantum gravity. This approach solves the Immirzi parameter problem occurring in the standard loop approach based on the $SU(2)$ gauge group. We show that there exists a unique loop quantization preserving all the classical symmetries at the quantum level and that the results obtained with it, such as the area operator spectrum, are independent of the Immirzi parameter. The standard $SU(2)$ approach violates the diffeomorphism invariance and is therefore an incorrect quantization of gravity.

Keywords: loop gravity, canonical quantization, BRST path integral.

DOI: 10.4213/tmf62

 English version: Theoretical and Mathematical Physics, 2004, 139:3, 751–765

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