Abstract
The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.
Highlights
Evident that the tools of quantum field theory — for example, the double copy — have interesting implications for classical physics
We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics
Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy
Summary
To connect three-point amplitudes to Newman-Penrose scalars, all that is needed is a direct computation using the methods of quantum field theory. The theta function ensures that quanta created around the vacuum have momenta directed into the future with respect to t1; in other words, they have positive energy with respect to this choice of time direction. Note that the wave packet is such that the uncertainties in the position and the momentum of our source are small. We will treat this scalar particle as a probe. We will not need a field operator for this state. Where the wave function φ(p) is sharply-peaked around the momentum pμ = muμ Note that in this case the theta function enforces positive energy along t2.
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