A one-dimensional massless scalar field coupled to a dispersive mirror models a jellium sheet coupled to electromagnetic waves propagating along the normal. The quantum radiation emitted when the mirror moves [with velocity β(t)] exerts a reactioin force F. For β≪c, perturbation theory yields, without appeal to cutoffs or to regularization, the delayed response function ${\mathit{G}}_{\mathit{q}}$ of the mean-field momentum 〈q〉 to β and thence 〈F〉=-d〈q〉/dt. A finite inertial-mass shift is absorbed by renormalization. Alternatively, the Fourier transform of ${\mathit{G}}_{\mathit{q}}$ can be determined, up to renormalization, through its dispersion representation; the requisite input is its imaginary part, supplied via the fluctuation-dissipation theorem by the fluctuations of the force on a stationary mirror. Unfortunately, without stepping outside a strictly local theory, one cannot define a useful response function linking 〈F〉 directly to β.

• Received 5 July 1994

DOI:https://doi.org/10.1103/PhysRevA.51.3506