  The paper contains further development of the idea of field quantization
introduced in M. Czachor, J. Phys. A: Math. Gen. {\bf 33} (2000) 8081-8103. The
formalism is extended to the relativistic domain. The link to the standard
theory is obtained via a thermodynamic limit. Unitary representations of the
Poincar\'e group at the level of fields and states are explicitly given.
Non-canonical multi-photon and coherent states are introduced. In the
thermodynamic limit the statistics of photons in a coherent state is
Poissonian. The $S$ matrix of radiation fields produced by a classical current
is given by a non-canonical coherent-state displacement operator, a fact
automatically eliminating the infrared catastrophe. Field operators are shown
to be operators and not operator-valued distributions, and can be multiplied at
the same point in configuration space. An exactly solvable example is used to
compare predictions of the standard theory with those of non-canonical quantum
optics, and explicitly shows the mechanism of automatic ultraviolet
regularization occuring in the non-canonical theory. Similar conclusions are
obtained in perturbation theory, where one finds the standard Feynman diagrams,
but the Feynman rules are modified. A comparison with the Dicke-Hepp-Lieb model
allows to identify the physical structure behind the non-canonical algebra as
corresponding to an ensemble of indefinite-frequency oscillators with constant
density $N/V$.
