Quasiboson excitation spectrum of the relativistic quantum scalar plasma in the Hartree-Vlasov approximation

Using plasma-physics techniques (e.g., covariant Wigner functions) the excitation spectrum of the quasibosons within the so-called relativistic quantum scalar plasma (i.e., a system of spin-(1/2 fermions interacting with self-coupled scalar bosons via a Yukawa-type interaction) is derived both in the linearized Hartree-Vlasov approximation (random-phase approximation) and in perturbation at order 2. These spectra are compared and discussed in two cases: (i) in the ''semiclassical'' cases where vacuum effects are discarded and (ii) in the renormalized cases. Except at low densities where both perturbative and nonperturbative results agree, in general, strongly different behaviors occur