  The phenomenological Maxwell field is quantized for arbitrarily space- and
frequency-dependent complex permittivity. The formalism takes account of the
Kramers--Kronig relation and the dissipation-fluctuation theorem and yields the
fundamental equal-time commutation relations of QED. Applications to the
quantum-state transformation at absorbing and amplifying four-port devices and
to the spontaneous decay of an excited atom in the presence of absorbing
dielectric bodies are discussed.
