# An Inverse Scattering Problem for Dirac Equations with Time-Dependent Electromagnetic Potentials

### Hiroshi T. Ito

Ehime University, Matsuyama, Japan

## 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*: = {(*τ, ξ*) ∈ ℝ x ℝ3;|τ|<*c*|ξ|} 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.

## Cite this article

Hiroshi T. Ito, An Inverse Scattering Problem for Dirac Equations with Time-Dependent Electromagnetic Potentials. Publ. Res. Inst. Math. Sci. 34 (1998), no. 4, pp. 355–381

DOI 10.2977/PRIMS/1195144630