1207.2302 (Farrukh Chishtie et al.)

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

Farrukh Chishtie, D. G. C. McKeon

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 teritary 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.

View original: http://arxiv.org/abs/1207.2302