  The effect of particle creation by nonstationary external fields is
considered as a radiation effect in the expectation-value spacetime. The energy
of created massless particles is calculated as the vacuum contribution in the
energy-momentum tensor of the expectation value of the metric. The calculation
is carried out for an arbitrary quantum field coupled to all external fields
entering the general second-order equation. The result is obtained as a
functional of the external fields. The paper gives a systematic derivation of
this result on the basis of the nonlocal effective action. Although the
derivation is quite involved and touches on many aspects of the theory, the
result itself is remarkably simple. It brings the quantum problem of particle
creation to the level of complexity of the classical radiation problem. For
external fields like the electromagnetic or gravitational field there appears a
quantity, the radiation moment, that governs both the classical radiation of
waves and the quantum particle production. The vacuum radiation of an
electrically charged source is considered as an example. The research is aimed
at the problem of backreaction of the vacuum radiation.
