Superintense laser fields interacting with atoms require a relativistic description for the dynamics of the outer electrons. Quantum mechanically this implies the use of the Dirac equation. In its standard 3D form, however, the equation is untractable numerically and opaque to physical interpretation. Various approximations have been made. We present an alternative formulation of the equation, due to M. Boca, V. Florescu and M. Gavrila. This is based on introducing a relativistic generalization of the nonrelativistic space-translation transformation. The latter has been quite successful in the case of the Schrödinger equation, and has led to the discovery of new phenomena(e.g., atomic stabilization). For reference, we give a brief account of this case, also.Using the aforementioned transformation we have obtained the "generalized space-translated Dirac equation". Although quite complicated in itself, this equation proves to be tractable in the case of laser-atom interactions. We show that a solution of the equation, containing initially only low momenta ( p < < mc ), will maintain this property at all times, regardless of how intense the field is. Moreover, the equation splits into two independent Pauli equations, one describing the evolution of electronic, the other of positronic wave packets. When spin is ignored, these Pauli equations reduce to ordinary Schrödinger equations containing generalized potentials that are liable to extreme time-dependent distortion. The distortion of the generalized Coulomb potential is analyzed.
We emphasize that our final equation for the electron contains information that is equivalent to the original Dirac equation (if spin is ignored) and covers all current laser-atom interactions at frequencies w < < mc and for light atoms ( aZ < < 1 ). No pair production phenomena can occur, regardless of the intensity of the field.