# Quantizing the Palatini action using a transverse traceless propagator

## TL;DR

This paper quantizes the first order Einstein-Hilbert action using a path integral approach with specific gauge conditions, resulting in a simplified propagator and a manageable set of interacting fields and vertices.

## Contribution

It introduces a novel gauge fixing that yields a traceless, transverse graviton propagator and explicitly constructs the Feynman rules for all perturbative diagrams.

## Key findings

- Graviton propagator is both traceless and transverse.
- Feynman diagrams are built from five fundamental fields and vertices.
- The quantization scheme simplifies perturbative calculations.

## Abstract

We consider the first order form of the Einstein-Hilbert action and quantize it using the path integral. Two gauge fixing conditions are imposed so that the graviton propagator is both traceless and transverse. It is shown that these two gauge conditions result in two complex Fermionic vector ghost fields and one real Bosonic vector ghost field. All Feynman diagrams to any order in perturbation theory can be constructed from two real Bosonic fields, two Fermionic ghost fields and one real Bosonic ghost field that propagate. These five fields interact through just five three point vertices and one four point vertex.