Renormalization Group Approach to the Dynamical Casimir Effect

In this paper we study the one dimensional dynamical Casimir effect. We consider a one dimensional cavity formed by two mirrors, one of which performs an oscillatory motion with a frequency resonant with the cavity. The naive solution, perturbative in powers of the amplitude, contains secular terms. Therefore it is valid only in the short time limit. Using a renormalization group technique to resum these terms, we obtain an improved analytical solution which is valid for longer times. We discuss the generation of peaks in the density energy profile and show that the total energy inside the cavity increases exponentially.