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. Introduction.-The interaction between light and matter is an important part of modern physics, interesting from both a fundamental and an applied point of view. The investigation of the regime of strong light-matter coupling, where the interaction between photons and material excitations can not be treated perturbatively, is of special interest. One of the fundamental phenomena in this domain is the dynamic (AC) Stark effect [1] associated with the stationary energy shift of electron energy levels under the influence of an electromagnetic wave and taking place in both atomic systems and solids [2][3][4][5][6][7][8][9][10]. Particularly, the dynamic Stark effect opens stationary bandgaps in semiconductor systems, which take place in resonant points of the Brillouin zone satisfying the condition where the photon energy is equal to the energy interval between electron bands of the semiconductor. This gap can manifest itself in various physical effects [8][9][10].