Dynamical Casimir effect and loop corrections

We calculate quantum loop corrections to the stress-energy flux caused by moving mirrors. We consider massless, self-interacting, phi(4), real scalar theory. In these calculations we encounter new and quite unexpected subtleties due to the absence of global hyperbolicity in the presence of mirrors. We attempt to clearly phrase as many hidden assumptions and complications as possible that appear while solving the problem in question. On top of that, we find that quantum loop corrections to the stress-energy flux grow with time and are not suppressed in comparison with the semiclassical contributions. Thus, we observe the breakdown of the perturbation theory, and we discuss its physical origin and ways to deal with such a situation. As a byproduct, we observe a similarity of the problem in question with that for the minimally coupled, massless scalar field in de Sitter space.