Abstract
Weoutline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multigraviton, two-body, on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to nonanalytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering.
Highlights
Weoutline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multigraviton, two-body, on-shell scattering amplitudes between massive fields
We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the postMinkowskian expansion
Today it is universally accepted that classical general relativity can be understood as the ħ → 0 limit of a quantum mechanical path integral with an action that, minimally, includes the Einstein-Hilbert term
Summary
The long-distance terms we seek are precisely of such a nonanalypticffiffiffikffiffiiffiffinffi d, being functions of the dimensionless ratio m= −q2, where m is a massive probe, and qμ describes a suitably defined momentum transfer [4] This leads to the proposal that these modern methods be used to compute post-Newtonian and post-Minkowskian perturbation theory of general relativity for astrophysical processes such as binary mergers. While the framework for classical general relativity as described above would involve all possible interaction terms in the Lagrangian, ordered according to a derivative expansion, one can always choose to retain only the Einstein-Hilbert action Quantum mechanically this is inconsistent, but for the purpose of extracting only classical results from that action, it is a perfectly valid truncation. In Ref. [8], Damour proposed a new approach for converting classical scattering amplitudes into the
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