A light-fronts approach to a two-center time-dependent Dirac equation

The two center time dependent Dirac equation, for an electron in the extern al field of two colliding ultrarelativistic heavy ions is considered, In th e ultrarelativistic limit, the ions are practically moving at the speed of light and the electromagnetic fields of the ions arc confined to thc light fronts by the extreme Lorentz contraction and by the choice of gauge, desig ned to remove the long-range Coulomb effects. An exact solution to the ultr arelativistic limit of the two-center Dirac equation is found by using ligh t-front variables and a light-fronts representation. Previously unexplained experimental results obtained at CERN's SPS are explained in this way and predictions are made as to where one should look, in momentum space, and in space-time, if one wants to study and observe non-perturbative electromagn etic pair-production effects in extremely relativistic heavy-ion collisions .