Bethe-Salpeter equation for classical gravitational bound states

A bstract The Bethe-Salpeter equation is a non-perturbative, relativistic and covariant description of two-body bound states. We derive the classical for two massive point particles (with or without spin) in gravitational system. This recursion relation which involves two-massive-particle-irreducible diagrams space amplitudes, defined by quotienting out symmetrization over internal graviton exchanges. In this context, we observe that leading eikonal approximation to scattering arises directly from unitarity techniques with coherent state virtual gravitons. More generally, solve analytically at all orders exponentiating kernel impact parameter space. clarify connection between Hamilton-Jacobi action, making manifest analytic continuation observables. Using explicit resummations (spinless spinning) amplitudes momentum space, further explore poles energies residues wavefunctions. Finally, discuss analogue Sommerfeld enhancement occurs cross sections.