Shedding light on bound states with amplitudes

21.03.2023 14:00 – 15:00

Despite their fundamental importance in particle physics, bound states are often given relatively little attention in standard textbooks, with only a paragraph or a chapter dedicated to them. In contrast, a significant amount of research has focused on computing scattering observables. This highlights a gap in our understanding of the physics of bound systems, particularly from the perspective of quantum field theory. My aim is to address this issue using modern amplitude techniques, focusing on the case of classical gravitational bound states that are of particular relevance to the gravitational wave community. Specifically, we will derive and solve the classical Bethe-Salpeter (BS) equation for two massive point particles with and without spin in a bound gravitational system. The non-perturbative BS equation involves two-massive particle irreducible diagrams in the quotient space of classical amplitudes, defined from the symmetrization over the internal graviton exchanges. We will present a novel recursion relation for classical amplitudes, which can be solved analytically at all orders using the exponential of the classical kernel in impact parameter space. Then we will clarify the relationship between the kernel and the Hamilton-Jacobi action, demonstrating the analytical continuation between classical bound and unbound observables. Finally, we will perform the analytic resummation of classical amplitudes in momentum space, showing the relation of the poles with bound state energies and of the residues at the poles with the two-body decay rate, as well as discussing the relativistic analogue of the Sommerfeld effect.

Lieu

Bâtiment: Ecole de Physique

Room 234

entrée libre