Spin Resonance Effect on Pair Production in Rotating Electric Fields

We advance a new analytical method for the Dirac equation in two-dimensional, homogeneous, time-dependent electric fields, which expresses the Cauchy problem of the two-component spinor and its derivative as the time-ordered integral of the transition rate of the time-dependent eigenspinors and the time-dependent energy eigenvalues. The in-vacuum at later times evolves from that at the past infinity and continuously make transitions between eigenspinors and between positive and negative frequencies of the time-dependent energy eigenvalues. The production of electron and positron pairs is given by the coefficient of the negative frequency at the future infinity which evolves from the positive frequency at the past infinity. In the adiabatic case when the time scale for the rotation of eigenspinors and energy eigenvalues is much longer than the electron Compton time, we find the spin-resonance effect on the pair production, which is simply determined by the spin rotation, the pair production and the continuous transmission coefficients between the energy eigenvalues without the change of spin states.