Dynamics of Dollard asymptotic variables. Asymptotic fields in Coulomb scattering

Abstract

Generalizing Dollard’s strategy, we investigate the structure of the scattering theory associated to any large time reference dynamics [Formula: see text] allowing for the existence of Møller operators. We show that (for each scattering channel) [Formula: see text] uniquely identifies, for [Formula: see text], asymptotic dynamics [Formula: see text]; they are unitary groups acting on the scattering spaces, satisfy the Møller interpolation formulas and are interpolated by the [Formula: see text]-matrix. In view of the application to field theory models, we extend the result to the adiabatic procedure. In the Heisenberg picture, asymptotic variables are obtained as LSZ-like limits of Heisenberg variables; their time evolution is induced by [Formula: see text], which replace the usual free asymptotic dynamics. On the asymptotic states, (for each channel) the Hamiltonian can by written in terms of the asymptotic variables as [Formula: see text], [Formula: see text] the generator of the asymptotic dynamics. As an application, we obtain the asymptotic fields [Formula: see text] in repulsive Coulomb scattering by an LSZ modified formula; in this case, [Formula: see text], so that [Formula: see text] are free canonical fields and [Formula: see text].