The Plasmon in Hot $φ^4$ Theory

We study the 2-loop resummed propagator in hot $g^2\phi^4$ theory. The propagator has a cut along the whole real axis in the complex energy plane, but for small $g$, the spectral density is sharply peaked around the plasmon. The dispersion relation and the width of the plasmon are calculated at zero {\em and} finite momentum. At large momenta the spectral width vanishes, and the plasmon looses its collectivity and behaves like a non-interacting free particle.