  In this paper we developed the resolvent method for super-operator equations
with their applications in quantum optics. Our approach is based on the novel
concept of linear super-operator acting on the Hilbert subspace of vector or
scalar linear operators satisfying physically reasonable commutation relations.
The super-operator equations for the electromagnetic (EM) field operators are
formulated for the problems of quantum antenna emission and quantum light
scat-tering by a dielectric body. The general solution of super-operator
equation is presented in terms of the classical resolvent. In contrast to the
classical case, it includes the ancillary components associated with the
quantum noise even in the absence of absorption. The reason for it lies in the
energy exchange between different spatial regions with various bases for the
field presentation (it looks like losses or gain from the point of view of the
correspondent region). A number of examples (two-element dipole antenna, plane
dielectric layer, and dielectric cylinder with circular cross section) which
demonstrate the physical mechanism of the appearance of noise are considered.
It is shown, that antenna emission or scattering transforms the coherent
properties of quantum light. This opens a new way of controlling the coherence
in a direction dependent manner, a feature that can be useful in various
applications of quantum technologies, including, quantum radars and lidars, and
quantum antennas.
