As a step in approaching the problem of backreaction of the vacuum rad
iation, the energy of massless particles created from the vacuum by ex
ternal fields is calculated as a functional of these fields. The calcu
lation is done for a quantum field coupled to all external fields ente
ring the general second-order operator. The mechanism by which the qua
ntum noise gets averaged and the positive radiation energy obtains is
completely different from the one in two dimensions. For external elec
tromagnetic and gravitational fields there appears a quantity, the rad
iation moment, that governs both the radiation of classical waves and
the quantum particle production. (C) 1997 Elsevier Science B.V.