An enduring problem in the engineering of high-power semiconductor devices is how to mitigate the effect of heating. Heating means the proliferation of phonons, and phonons, interacting with electrons directly affect the electronic performance of the device. Nowhere is this more evident than the role of hot polar-optical phonons in reducing the drift velocity in the channel of an HFET and hence reducing its performance at high frequencies. The task of describing hot-phonon effects is complicated by the coupling to plasma modes. We present a theory of coupled plasmon-phonon modes in GaN, how they interact with electrons and how their lifetime becomes density-dependent. Raman scattering in bulk material shows a reduction of lifetime with increasing density and we offer an explanation for this in terms of the frequency dependence of the anharmonic decay mechanism. Hot-phonon effects, however, involve modes with wave-vectors beyond those probed by Raman scattering. By adopting a single-pole approximation for these modes we have obtained the lifetime dependence on wave vector, electron temperature and density.