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Path Integral Quantization of the First Order Einstein-Hilbert Action from its Canonical Structure
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We consider the form of the path integral that follows from canonical quantization and apply it to the first order form of the Einstein-Hilbert action in $d > 2$ dimensions. We show that this is inequivalent to what is obtained from applying the Faddeev-Popov (FP) procedure directly. Due to the presence of tertiary first class constraints, the measure of the path integral is found to have a substantially different structure from what arises in the FP approach. In addition, the presence of second class constraints leads to non-trivial ghosts, which cannot be absorbed into the normalization of the path integral. The measure of the path integral lacks manifest covariance.
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Cited by 2 Pith papers
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Covariant quantization of the Einstein-Hilbert theory in first-order form
A covariant BV quantization of first-order Einstein-Hilbert gravity is constructed, yielding a novel trivial symmetry and establishing on-shell quantum equivalence to the metric formulation.
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Covariant quantization of the Einstein-Hilbert theory in first-order form
A covariant path-integral quantization of first-order Einstein-Hilbert gravity is constructed using BV formalism, yielding structural identities from Dyson-Schwinger equations and equivalence to the second-order formu...
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