A canonical approach to Cherenkov radiation in the presence of a
magnetodielectric medium is presented in classical, nonrelativistic and
relativistic quantum regimes. The equations of motion for the canonical
variables are solved explicitly for both positive and negative times. Maxwell
and related constitute equations are obtained. In the large-time limit, the
vector potential operator is found and expressed in terms of the medium
operators. The energy loss of a charged particle, emitted in the form of
radiation, in finite temperature is calculated. A Dirac equation concerning the
relativistic motion of the particle in presence of the magnetodielectric medium
is derived and the relativistic Cherenkov radiation at zero and finite
temperature is investigated. Finally, it is shown that the Cherenkov radiation
in nonrelativistic and relativistic quantum regimes, unlike its classical
counterpart, introduces automatically a cutoff for higher frequencies beyond
which the power of radiation emission is zero.Comment: To be appear in PR