Asymptotic channels and gauge transformations of the time-dependent   Dirac equation for extremely relativistic heavy-ion collisions
  We discuss the two-center, time-dependent Dirac equation describing the dynamics of an electron during a peripheral, relativistic heavy-ion collision at extreme energies. We derive a factored form, which is exact in the high-energy limit, for the asymptotic channel solutions of the Dirac equation, and elucidate their close connection with gauge transformations which transform the dynamics into a representation in which the interaction between the electron and a distant ion is of short range. We describe the implications of this relationship for solving the time-dependent Dirac equation for extremely relativistic collisions. 
J. C. Wells (1 and 2), B. Segev (2), and J. Eichler (3) ((1) Center   for Computational Sciences, Oak Ridge National Laborat...