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arXiv · 1207.2302

Path Integral Quantization of the First Order Einstein-Hilbert Action from its Canonical Structure

Farrukh Chishtie·D. G. C. McKeon
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Abstract

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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Farrukh Chishtie, D. G. C. McKeon. 2012-11-11. Path Integral Quantization of the First Order Einstein-Hilbert Action from its Canonical Structure. https://doi.org/10.1088/0264-9381%2F29%2F23%2F235016

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