We present a formalism for computing classically measurable quantities directly from on-shell quantum scattering amplitudes. We discuss the ingredients needed for obtaining the classical result, and show how to set up the calculation to derive the result efficiently. We do this without specializing to a specific theory. We study in detail two examples in electrodynamics: the momentum transfer in spinless scattering to next-to-leading order, and the momentum radiated to leading order.-i -6.2.1 General expressions 54 6.2.

We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.

The double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory. Motivated by the importance of the relativistic two-body problem, we study the classical dynamics of colour-charged particle scattering from the perspective of amplitudes, rather than equations of motion. We explain how to compute the change of colour, and the radiation of colour, during a classical collision. We apply our formalism at next-to-leading order for the colour change and at leading order for colour radiation.

We show that the Newman-Janis shift property of the exact Kerr solution can be interpreted in terms of a worldsheet effective action. This holds both in gravity, and for the single-copy $$ \sqrt{\mathrm{Kerr}} $$ Kerr solution in electrodynamics. At the level of equations of motion, we show that the Newman-Janis shift holds also for the leading interactions of the Kerr black hole. These leading interactions are conveniently described using chiral classical equations of motion with the help of the spinor-helicity method familiar from scattering amplitudes.

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number $1\leq B\leq 8$ obtained by numerical simulation of the full field theory. For $9\leq B\leq 23$, a large number of static solutions of the point particle model are found, all closely resembling size $B$ subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.Comment: 33 page