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

摘要

The changes in the action (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 a factor of e~2 with changes in the action 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 change in the action 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 emergence of a real part in the change in the action is a direct consequence of causality, according to which Re #DELTA#_f(z,#mu#) not= 0 only for timelike and lightlike intervals.