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The action changes (and thus the vacuum conservation amplitudes) in theproper-time representation are found for an accelerated mirror interacting withscalar and spinor vacuum fields in 1+1 space. They are shown to coincide towithin the multiplier e^2 with the action changes of electric and scalarcharges accelerated in 3+1 space. This coincidence is attributed to the factthat the Bose and Fermi pairs emitted by a mirror have the same spins 1 and 0as do the photons and scalar quanta emitted by charges. It is shown that thepropagation of virtual pairs in 1+1 space can be described by the causalGreen's function \Delta_f(z,\mu) of the wave equation for 3+1 space. This isbecause the pairs can have any positive mass and their propagation function isrepresented by an integral of the causal propagation function of a massiveparticle in 1+1 space over mass which coincides with \Delta_f(z,\mu). In thisintegral the lower limit \mu is chosen small, but nonzero, to eliminate theinfrared divergence. It is shown that the real and imaginary parts of theaction change are related by dispersion relations, in which a mass parameterserves as the dispersion variable. They are a consequence of the same relationsfor \Delta_f(z,\mu). Therefore, the appearance of the real part of the actionchange is a direct consequence of the causality, according to which real partof \Delta_f(z,\mu) is nonzero only for timelike and zero intervals.Comment: 23 pages, Latex, revte

journal of experimental and theoretical physics

Common vacuum conservation amplitude in the theory of the radiation of mirrors in two-dimensional space-time and of charges in four-dimensional space-time