In this paper, the differential cross section for the Compton scattering process is calculated. Two types of corrections are investigated: corrections due to violation of Lorentz symmetry and thermal effects. An extended QED is considered to introduce the parameter that leads to the breaking of symmetry. While temperature effects are introduced using Thermofield Dynamics formalism. It is shown that the differential cross section changes with both corrections. These corrections are dominant at appropriate limits. These special cases are analyzed and compared with other results from the literature.
I. INTRODUCTIONQuantum Electrodynamics (QED) is the theory that deals with the interaction between elementary particles, such as fermions and photons. Compton scattering [1] is an example of the many scattering processes explained by QED. This process consists of an interaction between electrons and photons through an intermediate electron. The QED is a sector of the Standard Model (SM), which is considered the most complete theory about nature. The SM is built based on Lie group theories, having as its primary structure the product SU (3) × SU (2) × U (1) [2]. The SM describes elementary particles, their fundamental properties and their interactions, except gravity [3][4][5]. The fact that SM does not include gravity makes this theory incomplete with respect to the description of matter and its interactions. Such a situation suggests that SM is not fundamental, but effective.However, there are some theories that propose to deal with all fundamental forces, such as the string theory and supersymmetric models [4,6], among others.In string theory, Kostelecký and Samuel studied a process similar to the Higgs mechanism, looking for components of the tensor field that have a non-zero vacuum expectation value. It was then seen that this fact leads to a spontaneous violation of Lorentz symmetry in the theory