On an Exponential Representation of the Gravitational S-Matrix

Abstract

An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details. Computationally, rules are simple because pieces that must be subtracted are given by combinations of unitarity cuts. Analyzing classical gravitational scattering to third Post-Minkowskian order in both maximal supergravity and Einstein gravity we find agreement with other approaches, including the contributions from radiation reaction terms. The kinematical relation for the two-body problem in isotropic coordinates follows immediately from this procedure, again with the inclusion of radiation reaction pieces up to third Post-Minkowskian order.

26 pages. v2: minor corrections. Version to appear in JHEP

References in corpus (13)

• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• The Eikonal Approach to Gravitational Scattering and Radiation at $\mathcal{O}(G^3)$
• Energetics of two-body Hamiltonians in post-Minkowskian gravity
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Classical Gravity from Loop Amplitudes
• Radiative contributions to gravitational scattering
• Next-to-soft corrections to high energy scattering in QCD and gravity
• High-energy string-brane scattering: leading eikonal and beyond
• Rescattering corrections and self-consistent metric in Planckian scattering
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order
• Waveforms from Amplitudes

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• Linear Response, Hamiltonian and Radiative Spinning Two-Body Dynamics
• Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion
• Post-Minkowskian Radial Action from Soft Limits and Velocity Cuts
• Angular momentum of zero-frequency gravitons
• Exponentiation of the leading eikonal with spin
• Scattering Angles in Kerr Metrics
• Gravitational Bremsstrahlung with tidal effects in the post-Minkowskian expansion
• Eikonal amplitudes from curved backgrounds
• Scalar QED as a toy model for higher-order effects in classical gravitational scattering
• Classical vs Quantum Eikonal Scattering and its Causal Structure
• Gravitational Faraday effect from on-shell amplitudes
• Light bending from eikonal in worldline quantum field theory
• Bethe-Salpeter equation for classical gravitational bound states
• Angular Momentum Loss Due to Tidal Effects in the Post-Minkowskian Expansion
• All order gravitational waveforms from scattering amplitudes
• Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity
• Binary Dynamics from Worldline QFT for Scalar-QED
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Quantization Conditions and the Double Copy
• Classical gravitational scattering from a gauge-invariant double copy
• Classical physics from amplitudes on curved backgrounds
• Yang-Mills observables: from KMOC to eikonal through EFT
• Energetics and scattering of gravitational two-body systems at fourth post-Minkowskian order
• Effective-one-body formalism for leading-order radiative effects in the post-linear framework