Understand
The path integral is calculated for the statistical sum of the microcanonical ensemble in a generic time-parametrization invariant gravitational model with the Friedman-Robertson-Walker (FRW) metric.
- This represents the first example of a systematic calculation of the Faddeev-Popov gauge-fixed path integral in the minisuperspace sector of quantum cosmology.
- The gauge fixing procedure, together with gauging out local diffeomorphisms, also handles the residual symmetries associated with the conformal Killing vector of the FRW metric and incorporates the Batalin-Vilkovisky quantization technique for gauge theories with linearly dependent generators.
- For a subset of saddle-point instantons, characterized by a single oscillation of the FRW scale factor, this technique is designed to obtain the one-loop statistical sum in the recently suggested model of cosmological initial conditions generated by a conformal field theory with a large number of quantum species.