  Non-canonical quantization is based on certain reducible representations of
canonical commutation relations. Relativistic formalism for electromagnetic
non-canonical quantum fields is introduced. Unitary representations of the
Poincar\'e group at the level of fields and states are explicitly given.
Multi-photon and coherent states are introduced. Statistics of photons in a
coherent state is Poissonian if an appropriately defined thermodynamic limit is
performed. Radiation fields having a correct $S$ matrix are constructed. The
$S$ matrix is given by a non-canonical coherent-state displacement operator, a
fact automatically eliminating the infrared catastrophe. This, together with
earlier results on elimination of vacuum and ultraviolet infinities, suggests
that non-canonical quantization leads to finite field theories. Renormalization
constant $Z_3$ is found as a parameter related to wave functions of
non-canonical vacua.
