Trembling cavities in the canonical approach

We present a canonical formalism facilitating investigations of the dynamical Casimir effect by means of a response theory approach. We consider a massless scalar field confined inside of an arbitrary domain G (t), which undergoes small displacements for a certain period of time. Under rather general conditions a formula for the number of created particles per mode is derived. The perturbative approach reveals the occurrence of two generic processes contributing to the particle production: the squeezing of the vacuum by changing the shape and an acceleration effect due to motion of the boundaries. The method is applied to the configuration of moving mirror (s). Some properties as well as the relation to local Green's-function methods are discussed.