Radiative Corrections and the Palatini Action

TL;DR

This paper shows that radiative effects in General Relativity are equivalent whether using first-order or second-order Einstein-Hilbert actions, and introduces simplified Feynman rules for the first-order form.

Contribution

It demonstrates the equivalence of radiative effects in different formulations of the Einstein-Hilbert action and derives simplified Feynman rules for the first-order form.

Findings

Radiative effects are the same in first- and second-order formulations when tadpoles are discarded.

Simplified Feynman rules involve only two propagating fields and three vertices.

One-loop two-point function computed using the new rules confirms their effectiveness.

Abstract

By using the Faddeev-Popov quantization procedure, we demonstrate that the radiative effects computed using the first-order and second-order Einstein-Hilbert action for General Relativity are the same, provided one can discard tadpoles. In addition, we show that the first order form of this action can be used to obtain a set of Feynman rules that involves just two propagating fields and three three-point vertices; using these rules is considerably simpler than employing the infinite number of vertices that occur in the second-order form. We demonstrate this by computing the one-loop, two-point function.