Graviton-mediated scattering amplitudes from the quantum effective action

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.

Lorentzian quantum gravity and the graviton spectral function

“…Finally, we note that our findings open a door to investigate scattering amplitudes and unitarity of fully quantised gravity [24,40,[46][47][48][49]. The key building blocks for this are the timelike graviton propagator obtained here (Fig.…”

The derivative expansion in asymptotically safe quantum gravity: general setup and quartic order

“…Another road is the inclusion of form factors along the lines of [139,179], and discuss aspects of unitarity and causality of the theory e.g. in the context of scattering amplitudes [180,181]. This would also allow to compute spectral functions from the fully momentum-dependent background propagators [140].…”

Towards a Higgs mass determination in asymptotically safe gravity with a dark portal

“…In the presence of a fluctuating background, an analogous analytical continuation is not possible [126]. Thus, results on asymptotically safe gravity matter systems are obtained in a Euclidean setting; see [127] for a study that singles out a time direction and [128] for the analytic continuation of the graviton propagator about a flat background as well as [129][130][131][132] for discussions of the analyticity properties of this propagator in asymptotic safety.…”