Canonical analysis with no second-class constraints of $BF$ gravity with Immirzi parameter

Abstract

In this paper we revisit the canonical analysis of $BF$ gravity with the Immirzi parameter and a cosmological constant. By examining the constraint on the $B$ field, we realize that the analysis can be performed in a Lorentz-covariant fashion while utterly avoiding the introduction of second-class constraints during the whole process. Finally, we make contact with the description of the phase space of first-order general relativity in terms of canonical variables with manifest Lorentz covariance subject to first-class constraints only recently introduced.

arXiv commentCorrected typos, added references

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Cited by in corpus (3)

• Straightforward Hamiltonian analysis of $BF$ gravity in $n$ dimensions
• Trace-free Einstein gravity as two interacting constrained $BF$ theories
• Canonical analysis of $BF$ gravity in $n$ dimensions