A classical interaction picture defines the classical eikonal directly in classical mechanics and yields all-order eikonal formulas for relativistic probes in EM and gravitational backgrounds.
Murua, The hopf algebra of rooted trees, free lie algebras, and lie series , Foundations of Computational Mathematics 6 (2006) 387
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Classical eikonal in relativistic scattering
A classical interaction picture defines the classical eikonal directly in classical mechanics and yields all-order eikonal formulas for relativistic probes in EM and gravitational backgrounds.