Unity of scattering amplitude and worldline approaches to binary dynamics

Mao Zeng  - Edinburgh University
Unity of scattering amplitude and worldline approaches to binary dynamics

Abstract
The rapid advance in gravitational wave detectors has spurred renewed interest in the two-body problem in general relativity. The perturbative regime, covering a large number of orbit cycles in future detectors like LISA, has enjoyed improved understanding from relativistic quantum field theory methods. Two main approaches have emerged, one based on scattering amplitudes in second-quantized theory and the other based on worldlines in first-quantized theory. We argue that despite their very different formulations, the two approaches are equivalent at an intimate level. In particular, by systematic algebraic manipulations, the loop integrand in the Kosower-Maybe-O'Connell formalism based on wavepacket scattering becomes identical to the counterpart in the worldline QFT formalism of Mogull et al., at least in simple models we studied. Our main method is a worldline interpretation of scattering amplitudes through the Schwinger parametrization of propagators. Different diagrams in the amplitude are combined into the same worldline integrand with different ordering of vertices. This also manifests the cancellations of divergences in the amplitudes which are required to give well-defined classical observables.

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