  Interactions between a source of light and atoms are ubiquitous in nature.
The study of them is interesting on the fundamental level as well as for
applications. They are in the core of Quantum Information Processing tasks and
in Quantum Thermodynamics protocols. However, even for two-level atom
interacting with field in rotating wave approximation there exists no exact
solution. This touches as basic problem in quantum field theory, where we can
only calculate the transitions in the time asymptotic limits (i.e. minus and
plus infinity), while we are not able to trace the evolution. In this paper we
want to get more insight into the time evolution of a total system of a
two-level atom and a continuous-mode quantum field. We propose an
approximation, which we are able to apply systematically to each order of Dyson
expansion, resulting in greatly simplified formula for the evolution of the
combined system at any time. Our tools include a proposed novel, {\it
non-Hermitian} re-normalization method. As a sanity check, by applying our
framework, we derive the known optical Bloch equations.
