It is well-known that the properties of elementary particles are modified when they propagate in a medium, as they become ‘dressed’ by their interactions: they acquire, for example, an effective mass which is different from the mass as measured in the vacuum. More generally, one speaks of the propagation of collective modes, or quasi-particles; in some cases, these quasi-particles can easily be identified with ordinary particles whose properties are only slightly modified by their interactions with the medium. In other cases collective modes bear little resemblance with particles in the vacuum.

Collective modes are characterized by a dispersion law ω(q) giving their energy ω as a function of their momenta q. Their lifetime is not infinite, contrary to that of stable particles in the vacuum; thus another relevant quantity is the decay (or damping) rate γ(q) of the collective modes.

In general, collective modes appear mathematically as poles of propagators with well-defined quantum numbers in the complex plane of the energy: the real part of the pole gives the dispersion law, while the imaginary part gives the damping rate; see, however, the remarks following (6.19). In the present chapter we shall study the propagation of gauge bosons and fermions in a plasma, and we shall compute explicitly the dispersion laws to a first approximation.