orrection to the quantum relation of photons involved in the Doppler effect in the framework of a special Lorentz violation model

he possibility of Lorentz symmetry breaking has been discussed in many models of quantum gravity. In this paper we followed the Lorentz violation model in Ref. 14 to discuss the Doppler frequency shift of photons and the Compton scattering process between photons and electrons, pointing out that following the idea in Ref. 14 we have to modify the usual quantum relation of photons involved in Doppler effect. But due to the current limited information and knowledge, we couldn’t yet determine the specific expression for the correction coefficient?of the quantum relation?of photons. However, the phenomenon of spontaneous radiation in a cyclotron maser?give us an opportunity to see what the expression for this correction coefficient?might look like, as the phenomenon of spontaneous radiation in a cyclotron maser can be explained by the Doppler effect of virtual photons and the Compton scattering process between virtual photons and electrons (or other particles). Therefore, under some restrictive conditions, we construct a very concise expression for this correction coefficient by discussing different cases. And then we used this expression to analyze the wavelength of radiation in the cyclotron maser, which tends to be a limited value at v→c, rather than to be 0 as in the Lorentz model. And we also discussed the?inverse Compton scattering phenomenon and found that there is a limit to the maximum energy that can be obtained by photons in the collision between ultra-high energy particles and low-energy photons, which conclusion is also very different from that obtained from the Lorentz model, in which the energy that can be obtained by the photon tends to be infinite as the velocity of particle is close to c. This paper still inherits the idea in Ref. 14 that the energy and momentum of particles (i.e., any particles, including photons) cannot be infinite, otherwise it will make some physical scenarios meaningless, and this view is also from the idea in some quantum gravity models. When the parameter Q?characterizing the degree of deviation from the Lorentz model is equal to 0, all the results and conclusions in this paper will return to the case as in the Lorentz model,?so this paper also provides us with a possible experimental scheme to determine the value of Q in Ref. 14 , although it still requires extremely high experimental energy.