Scattering by Magnetic Fields at Large Separation Klein-Gordon equations is studied in the Sobolev space Hs = Hs(

In this work we consider the scattering by two magnetic fields with compact support in two dimensions and we analyse the asymptotic behavior of scattering amplitude when the distance between two centers of fields goes to infinity. Even if magnetic fields are of compact support, the magnetic potentials associated with fields do not necessarily fall off rapidly at infinity in the two dimensional space R. This is due to the elementary topological fact that R \ {0} is not simply connected. In quantum mechanics, magnetic potentials have a direct significance to the motion of particles as opposed to classical mechanics where the motion is governed only by magnetic fields. This remarkable property is well known as the Aharonov–Bohm effect ([2]). We study how this quantum effect is reflected in the scattering by magnetic fields at large separation. There are many physical literatures on the magnetic scattering in connection to the Aharonov–Bohm effect. We refer to the recent book [1]. A lot of references related to the subject can be found there.