Abstract- In this paper relativistic Cerenkov radiation was studied in a 3-D magneto-dielectric medium.The dielectric function permeability of the medium are assumed to satisfy Kramers-Kronig equations.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.it is calculated the losing energy longitudinal with using the transition probability term in the Fermi”s golden rule.

Keywords: Cerenkov radiation, Fermie’s golden rule.

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