New representation and a vacuum state for canonical quantum gravity

TL;DR

This paper introduces a new geometric representation for canonical quantum gravity and supergravity that avoids the singular metric problem and aligns with the Wheeler-DeWitt framework, offering a formal vacuum state.

Contribution

It presents a novel representation combining advantages of Ashtekar's and Wheeler-DeWitt approaches, with a modified quantization method to address anomalies.

Findings

A new geometric representation free of singular metrics.

A formal vacuum state functional with quantum field theory features.

Recovery of the Wheeler-DeWitt equation with an anomaly correction.

Abstract

A new representation for canonical gravity and supergravity is presented, which combines advantages of Ashtekar's and the Wheeler~DeWitt representation: it has a nice geometric structure and the singular metric problem is absent. A formal state functional can be given, which has some typical features of a vacuum state in quantum field theory. It can be canonically transformed into the metric representation. Transforming the constraints too, one recovers the Wheeler~DeWitt equation up to an anomalous term. A modified Dirac quantization is proposed to handle possible anomalies in the constraint algebra.