Wheeler-DeWitt equation and Feynman diagrams

TL;DR

This paper develops a systematic expansion method in canonical quantum gravity that reproduces Feynman diagrams with graviton loops, revealing back reaction effects and connecting canonical and covariant approaches.

Contribution

It introduces a systematic expansion of constraint equations in quantum gravity that explicitly links canonical and covariant frameworks through Feynman diagrams.

Findings

Reproduces Feynman diagrams with graviton loops from canonical quantum gravity.

Explicitly shows back reaction effects of matter and vacuum polarization.

Establishes a correspondence between canonical and covariant quantum gravity.

Abstract

We present a systematic expansion of all constraint equations in canonical quantum gravity up to the order of the inverse Planck mass squared. It is demonstrated that this method generates the conventional Feynman diagrammatic technique involving graviton loops and vertices. It also reveals explicitly the back reaction effects of quantized matter and graviton vacuum polarization. This provides an explicit correspondence between the frameworks of canonical and covariant quantum gravity in the semiclassical limit.