Graviton scattering amplitudes in first quantisation

TL;DR

This paper reviews first quantised methods, including string-inspired and worldline formalisms, for calculating graviton scattering amplitudes, highlighting their simplification and efficiency over traditional Feynman diagram approaches.

Contribution

It introduces and compares first quantised techniques, demonstrating their advantages in simplifying graviton amplitude calculations compared to conventional methods.

Findings

First quantised approaches reduce computational complexity.

Worldline formalism offers compact amplitude expressions.

String-inspired methods provide pedagogical insights.

Abstract

We give a pedagogical review to alternative, first quantised approaches to calculating graviton scattering amplitudes, giving an introduction to string inspired approaches and presenting more recent work based on the worldline formalism of quantum field theory that is motivated by these historic results. We describe how these first quantised techniques can greatly simplify the determination of such amplitudes, in particular reducing the number of Feynman-like diagrams that enter the computation and leading to compact results.