Graviton-Mediated Scattering Amplitudes from the Quantum Effective Action

TL;DR

This paper develops a gauge-invariant formalism using the quantum effective action to compute graviton-mediated scattering amplitudes for non-minimally coupled scalars, ensuring quantum corrections meet physical consistency conditions.

Contribution

It introduces a novel curvature expansion approach that captures all quantum corrections and demonstrates its compatibility with unitarity, causality, and UV-finiteness without non-localities or extra degrees of freedom.

Findings

Formalism parameterizes quantum corrections comprehensively.

Explicit construction shows compatibility with physical constraints.

Framework applies to various quantum gravity models.

Abstract

We employ the curvature expansion of the quantum effective action for gravity-matter systems to construct graviton-mediated scattering amplitudes for non-minimally coupled scalar fields in a Minkowski background. By design, the formalism parameterises all quantum corrections to these processes and is manifestly gauge-invariant. The conditions resulting from UV-finiteness, unitarity, and causality are analysed in detail and it is shown by explicit construction that the quantum effective action provides sufficient room to meet these structural requirements without introducing non-localities or higher-spin degrees of freedom. Our framework provides a bottom-up approach to all quantum gravity programs seeking for the quantisation of gravity within the framework of quantum field theory. Its scope is illustrated by specific examples, including effective field theory, Stelle gravity, infinite derivative gravity, and Asymptotic Safety.