Worldline Quantum Field Theory Unitarity Enables Multi-Loop Scattering Calculations in General Relativity

Understanding how massive objects interact through gravity remains a fundamental challenge in physics, and recent work by Kays Haddad, Gustav Uhre Jakobsen, and Gustav Mogull, along with Jan Plefka, advances our ability to model these interactions with unprecedented precision. The team, based at Humboldt-Universität zu Berlin and Queen Mary University of London, develops a new framework within Worldline Field Theory to describe the scattering of spinning compact bodies, such as black holes, in the strong gravity regime. This research establishes a clear connection between Worldline Field Theory and more traditional amplitude-based methods, demonstrating how unitarity, a principle ensuring the consistency of quantum mechanics, can be used to efficiently calculate complex gravitational effects. By completing the full on-shell action, including energy loss through gravitational waves and accounting for interactions between the spins of the bodies, the team achieves a significant step forward in accurately predicting the dynamics of these extreme gravitational systems.

This allows scientists to efficiently compute interactions, particularly in strong gravity regimes, and focus on the relevant degrees of freedom at a given energy scale. The use of worldline or path integral methods, representing particles as paths in spacetime and calculating interactions by integrating over these paths, is central to this work. This approach is well-suited for incorporating spin effects and bridging quantum field theory and classical gravity. The Post-Minkowskian expansion is widely utilized to approximate solutions to general relativity, enabling calculations of conservative and radiative effects in binary systems.

Compact Body Dynamics at 3PM Order

Scientists have achieved a significant breakthrough in calculating the dynamics of compact bodies, extending the on-shell action formalism within WQFT to an unprecedented order of accuracy. The research establishes a concrete link between WQFT and amplitude-based methods, confirming equivalence between on-shell actions derived from either approach through unitarity cuts. The team completed the full on-shell action, including dissipative terms, at 3PM order and up to quartic spin interactions on both massive bodies. This work builds upon a WQFT approach that combines first and second-quantised degrees of freedom, directly targeting classical contributions and enabling efficient calculations of scattering observables.

Researchers derived scattering observables, including momentum impulse and spin kick, using a real on-shell action constructed from vacuum diagrams with causal propagators. They successfully adapted generalised unitarity techniques to WQFT, allowing for efficient multi-loop contributions and calculations up to quartic order in spin. Measurements confirm the successful implementation of bosonic oscillators on the worldline, encoding the spin tensor and ensuring conservation of the covariant spin-supplementary condition. Furthermore, the research extends the non-spinning scattering dynamics to 5PM order with first-order contributions from the gravitational self-force, bringing scientists closer to a complete picture of scattering dynamics.

Spin and Dissipation in Compact Object Scattering

This work presents a significant advance in calculating the dynamics of compact objects, such as black holes and neutron stars, as they interact through gravity. Researchers have developed a method, based on WQFT, to determine how these objects scatter and exchange energy and momentum. The team successfully constructed a mathematical description, known as the on-shell action, which accurately predicts scattering outcomes, including the change in momentum and spin of the interacting bodies, up to a high degree of precision in a post-Minkowskian expansion. This achievement extends the current state-of-the-art by incorporating dissipative effects and accounting for interactions involving the spin of both bodies, up to quartic order.

The researchers also demonstrated a strong connection between their WQFT approach and alternative methods based on quantum field theory, confirming the consistency of both frameworks. Importantly, they adapted techniques from quantum field theory, specifically generalised unitarity, to efficiently calculate complex interactions within the WQFT framework. This allows for more rapid and accurate predictions of gravitational wave signals emitted during the scattering of compact objects.

The research also investigates spin-orbit and spin-spin interactions, crucial for accurately modelling the effects of spin in binary systems. Scientists address the challenges of defining the center of mass and momentum for spinning particles. Recent studies have calculated spin magnitude change during orbital evolution, a subtle but potentially observable effect arising from the interaction of spins with the orbit. Furthermore, researchers are working on calculating radiation reaction forces for spinning black holes and pushing calculations to higher orders in spin, crucial for achieving the accuracy needed for gravitational wave detection.