Particle and energy creation by moving mirrors

We consider the creation of massless scalar particles by a moving mirror in two-dimensional space-time. The correct form for the Bogoliubov coefficients is given and their high-frequency behavior is investigated. We next consider the energy radiated by the mirror and show that this is related in the expected way to the number of particles produced only if a particular condition on the trajectory is fulfilled. The well-known moving-mirror formula of Fulling and Davies, which gives the radiated energy as a functional of the mirror trajectory, is here rederived from the Bogoliubov transformation, without recourse to regularization. Finally we analyze the response of a particle detector, and solve the paradox of how the detector can respond even when the mirror is radiating no energy.