Resonant parts of nonlinear response tensors

It is pointed out that ambiguities arise in taking the resonant parts of nonlinear response tensors. A prescription is proposed and used to evaluate the resonant parts explicitly in terms of a covariant and gauge invariant formalism. Symmetry properties of the resonant parts are identified. The prescription used can be justified by analogy with a calculation based on QED where no ambiguity arises; it is also justified directly by classical arguments. In some standard treatments of nonlinear damping processes a necessary symmetry is not imposed. When this symmetry is imposed, the relations derived here imply that turbulent bremsstrahlung, as defined by Tsytovich et al., does not exist.