  The action changes (and thus the vacuum conservation amplitudes) in the
proper-time representation are found for an accelerated mirror interacting with
scalar and spinor vacuum fields in 1+1 space. They are shown to coincide to
within the multiplier e^2 with the action changes of electric and scalar
charges accelerated in 3+1 space. This coincidence is attributed to the fact
that the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0
as do the photons and scalar quanta emitted by charges. It is shown that the
propagation of virtual pairs in 1+1 space can be described by the causal
Green's function \Delta_f(z,\mu) of the wave equation for 3+1 space. This is
because the pairs can have any positive mass and their propagation function is
represented by an integral of the causal propagation function of a massive
particle in 1+1 space over mass which coincides with \Delta_f(z,\mu). In this
integral the lower limit \mu is chosen small, but nonzero, to eliminate the
infrared divergence. It is shown that the real and imaginary parts of the
action change are related by dispersion relations, in which a mass parameter
serves as the dispersion variable. They are a consequence of the same relations
for \Delta_f(z,\mu). Therefore, the appearance of the real part of the action
change is a direct consequence of the causality, according to which real part
of \Delta_f(z,\mu) is nonzero only for timelike and zero intervals.
