On the fluctuations of the Casimir forces. II. The stress-correlation function

For pt.I see ibid., vol.24, p.991 (1991). The quantized Maxwell field in a halfspace exerts stresses on the boundary plane, whose zero-point fluctuations are analyzed for a perfectly-conducting surface. The stress-correlation function on the surface is determined: its Fourier transform with respect to time and distance governs the mean-square deviation of the stress averaged over finite areas (diameters of order a) and over finite times of order T. Conditions guaranteeing physically sensible results are specified on the Fourier transforms of the averaging functions, with a systematic expansion for a/cT<<1, and the first few terms of an asymptotic approximation for a/cT>>1. The small-time behaviour of the surface-averaged correlation function appears to present a paradox which is elucidated. Finally, a very simple expression is found to leading order for the mean-square fluctuating force on perfectly conducting large bodies of arbitrary shape.