Transformation of Small-Signal Energy and Momentum of Waves

The transformation of the small-signal energy and momentum of a wave between two inertial reference frames as first given by Sturrock are derived by using simple perturbation theory and the appropriate transformations of length, time, current, and electromagnetic fields. The approach allows a straightforward generalization to the case of relativistic linear transformations and to nonrelativistic transformations between two reference frames that rotate with respect to each other. These rotating and linear transformations allow one to make very general statements about the frequency and wavenumbers for which negative-energy waves are obtained in a rotating and translating medium, as, for example, an electron beam in Brillouin flow.