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Generalized Kodama states. V. Evidence of the normalizability and renormalizability of 4D QGRA (Part II).

This is the sixth paper in the series outlining an algorithm to consistently quantize four-dimensional gravity. In this work we transform the pure Kodama state into the metric representation for the Bianchi IX minisuperspace model. Previous such calculations have been carried out to semiclassical order for a particular choice of gauge, revealing the existence of five topologically distinct states in the metric representation. We have performed our calculation to all orders in perturbation theory by maintaining the gauge degrees of freedom explicit, revealing the existence of a sixth state. We propose a resolution to the issue of reality conditions for the Ashtekar variables, and also for the recast-ing of 4-dimensional general relativity as a renormalizable field theory, stemming from the nonperturbative result obtained from this work. We also address the issue of normalizability of the Kodama state.