Unitarity and the On-Shell Action of Worldline Quantum Field Theory

A bstract We develop the on-shell action formalism within Worldline Quantum Field Theory (WQFT) to describe scattering of spinning compact bodies in General Relativity in the post-Minkowskian (PM) expansion. The real on-shell action is constructed from vacuum diagrams with causal (retarded) propagators from which scattering observables such as momentum impulse and spin kick follow via Poisson brackets of the initial scattering data. Furthermore, we explore the implications of unitarity at the level of the worldline and show how generalised unitarity techniques can be adapted to WQFT to efficiently compute multi-loop contributions. Our work establishes a concrete link between WQFT and amplitude-based methods, elucidating how unitarity cuts ensure equivalence between the on-shell action derived from either approach. Extending the state-of-the-art, we complete the full on-shell action — including dissipative terms — at (formal) 3PM order and up to quartic spin interactions on both massive bodies.