  We consider theoretically a semiconductor nanostructure embedded in
one-dimensional microcavity and study the modification of its electron energy
spectrum by the vacuum fluctuations of the electromagnetic field. To solve the
problem, a non-perturbative diagrammatic approach based on the Green's function
formalism is developed. It is shown that the interaction of the system with the
vacuum fluctuations of the optical cavity opens gaps within the valence band of
the semiconductor. The approach is verified for the case of large photon
occupation numbers, proving the validity of the model by comparing to previous
studies of the semiconductor system excited by a classical electromagnetic
field. The developed theory is of general character and allows for unification
of quantum and classical descriptions of the strong light-matter interaction in
semiconductor structures.
