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 dyn amics 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, a nd elucidate their close connection with gauge transformations which transf orm 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 ext remely relativistic collisions. [S1050-2947(99)03801-9].