The Čerenkov Effect and the Dielectric Constant

A quantum-mechanical theory of the {C} {C}{}erenkov radiation is developed wherein the refractive medium is treated not as a continuum but as an aggregation of atoms. The atoms and the electromagnetic field are considered as forming a single system which interacts with an incident charged particle. The {C} {C}{}erenkov radiation arises in first-order transitions induced by this interaction. The nature of this process suggests a quantum-mechanical definition of the dielectric constant with the aid of which the theory yields the well-known properties of the {C} {C}{}erenkov radiation. The definition of the dielectric constant is shown to lead to the same expression for this quantity as is given by the Kramers-Heisenberg dispersion formula.