Infrared Problem vs Gauge Choice: Scattering of Classical Dirac Field

We consider the Dirac equation for classical spinor field placed in an external, time-dependent electromagnetic of form typical scattering settings: $F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$, where current producing $F^{\mathrm{ret}/\mathrm{adv}}$ has past and future asymptotes homogeneous degree $-3$, free fields $F^{\mathrm{in}/\mathrm{out}}$ are radiation produced by currents with similar asymptotic behavior. show existence gauges which particle 'in' 'out' states approaching states, no long-time corrections dynamics. Using a special Cauchy foliation spacetime we this context completeness wave operators. Moreover, define 'evolution picture' evolution operator well-defined limits $t\to\pm\infty$, thus operators do not need counteraction.