Compton Scattering in the Presence of Lorentz and CPT Violation

We examine the process of Compton scattering, in the presence of a Lorentz- and CPT-violating modification to the structure of the electron. We calculate the complete tree-level contribution to the cross section; our result is valid to all orders in the Lorentz-violating parameter. We find a cross section that differs qualitatively from the Klein-Nishina result at small frequencies, and we also encounter a previously undescribed complication that will arise in the calculation of many Lorentz-violation cross sections: The Lorentz violation breaks the spin degeneracy of the external states, so we cannot use a closure relation to calculate the unpolarized cross section.