Abstract
In this paper, we show that there is a Non‐Commutative Plane (NCP) in the perpendicular magnetic fields in the accelerator, and the QED with NCP (QED‐NCP) has been formulated. Being similar to the theory of quantum Hall effects, an effective filling factor f(B) is introduced, which characters the possibility occupied the LLL state by the electrons living on NCP. The back Compton scattering amplitudes of QED‐NCP are derived, and the differential cross sections for the process with fixed initial polarizing electrons and photons are calculated. We propose to precisely measure the polarization dependent differential cross sections of the back Compton scattering in the perpendicular magnetic fields experimentally, which may lead to reveal the effects of QED with NCP. This should be interesting and remarkable. The existing Spring‐8’s data have been analyzed primitively, and some hints for QED‐NCP effects are seen.
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