Backward Compton Scattering and QED with Noncommutative Plane in the Strong Uniform Magnetic Field

In the strong uniform magnetic field, the noncommutative plane (NCP) caused by the lowest Landau level (LLL) effect, and QED with NCP (QED-NCP) are studied. Being similar to the condensed matter theory of quantum Hall effect, an effective filling factor $f(B)$ is introduced to character the possibility that the electrons stay on the LLL. The analytic and numerical results of the differential cross section for the process of backward Compton scattering in the accelerator with unpolarized or polarized initial photons are calculated. The existing data of BL38B2 in Spring-8 have been analyzed roughly and compared with the numerical predictions primitively. We propose a precise measurement of the differential cross sections of backward Compton scattering in a strong perpendicular magnetic field, which may lead to reveal the effects of QED-NCP.