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

In this paper we followed the idea in Ref. 1 to discuss the Doppler frequency shift of photons and the Compton scattering between photons and electrons, pointing out that followingthe idea we have to modify the usual quantum relation of massless particle. But due to limitedinformation and knowledge, we couldn’t yet determine the specific expression for the correctioncoefficient of the quantum relation of massless particle. However, the phenomenon of spontaneous radiation in a cyclotron maser give us an opportunity to see what the expression for this correctioncoefficient might look like, as the phenomenon of spontaneous radiation in a cyclotron maser canbe explained by the effect of Doppler frequency shift of virtual photons and Compton scatteringbetween virtual photons and electrons. Therefor, 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 toa limited value at v→c, rather than to 0 as in the Lorentz model. This paper still inherits the idea inRef. 1 that the energy and momentum of particles cannot be infinite, otherwise it will make some equations meaningless, and this view is also from the idea in some quantum gravity models. This paper also provides us with a possible experimental scheme to determine the value of Qin Ref. 1 , but it still requires extremely high experimental energy.