In this paper relativistic Cerenkov radiation was studied in the form of explicit Green's function in a 3-D magneto-dielectric medium.The dielectric function permeability of the medium are assumed to satisfy Kramers-Kronig equations. In order to quantize electromagnetic field with integration of the Maxwell's equations in the coulomb gauge and a zero scalar potential, wave equation for vector potential is achieved. we use Fourier transform to solve the equation in Momentum space. It is introduced the new intraction Hamiltonian which is different from Hamiltonian term in non- relativistic state based on quantized electromagnetic field and second quantization method. components of the vector potential is calculated in terms of the Green's function.It is calculated the losing energy longitudinal with using the transition probability term in the Fermi”s golden rule. It is remarkable that the lateral component isn't different in the relativistic state.The results will be compared with earlier work(non- relativistic and non-magneto).

Keywords: Cerenkov radiation, Fermie’s golden rule

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