Abstract
We consider an inverse scattering problem, by using a time-dependent method, for the Dirac equation with a time-dependent electromagnetic field. The Fourier transform of the field is reconstructed from the scattering operator on a Lorents invariant set (0.1) D: = {(T,&€=R*R3M<c\ft} in the dual space of the space-time. As corollaries of this result, we can reconstruct the electromagnetic field completely if it is a finite sum of fields each of which is a time-independent one by a suitable Lorentz transform, and we can also determine the field uniquely if the fields satisfies some exponential decay condition. Our assumptions and results are independent of a choice of inertial frames.
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