Factorization and polarization in linearized gravity

TL;DR

This paper analyzes four-body graviton interactions in linearized gravity, demonstrating that gauge and Lorentz invariance lead to factorized scattering amplitudes and exploring polarization effects.

Contribution

It explicitly shows the factorization of four-body graviton scattering amplitudes due to gauge and Lorentz invariance in linearized gravity.

Findings

Scattering amplitudes are factorized by gauge and Lorentz invariance.

Polarization effects are analyzed using covariant density matrix formalism.

Results exclude spin-3/2 cases in the analysis.

Abstract

We investigate all the four-body graviton interaction processes: $gX\rightarrow \gamma X$, $gX\rightarrow gX$, and $gg\rightarrow gg$ with $X$ as an elementary particle of spin less than two in the context of linearized gravity except the spin-3/2 case. We show explicitly that gravitational gauge invariance and Lorentz invariance cause every four-body graviton scattering amplitude to be factorized. We explore the implications of this factorization property by investigating polarization effects through the covariant density matrix formalism in each four-body graviton scattering process.