A Bianchi-identity-based covariance test shows effective loop quantum gravity models need quantum-corrected 'emergent' metrics, not just corrected Hamiltonians, to be generally covariant.
Ashtekar, Symmetry reduced loop quantum gravity: A bi rd’s eye view
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Testing general covariance in effective models motivated by Loop Quantum Gravity
A Bianchi-identity-based covariance test shows effective loop quantum gravity models need quantum-corrected 'emergent' metrics, not just corrected Hamiltonians, to be generally covariant.