Vacuum radiation in covariant perturbation theory

As a step in approaching the problem of backreaction of the vacuum radiation, the energy of massless particles created from the vacuum by external fields is calculated as a functional of these fields. The calculation is done for a quantum field coupled to all external fields entering the general second-order operator. The mechanism by which the quantum noise gets averaged and the positive radiation energy obtains is completely different from the one in two dimensions. For external electromagnetic and gravitational fields there appears a quantity, the radiation moment, that governs both the radiation of classical waves and the quantum particle production.