  This work investigates the physics of elementary excitations for the
so-called relativistic quantum scalar plasma system, also known as the
Higgs-Yukawa system. Following the Nemes-Piza-Kerman-Lin many-body procedure,
the Random-Phase Approximation (RPA) equations were obtained for this model by
linearizing the Time-Dependent Hartree-Fock-Bogoliubov equations of motion
around equilibrium. The resulting equations have a closed solution, from which
the spectrum of excitation modes are studied. We show that the RPA oscillatory
modes give the one-boson and two-fermion states of the theory. The results
indicate the existence of bound states in certain regions in the phase diagram.
Applying these results to recent LHC observations concerning the mass of the
Higgs boson, we determine limits for the intensity of the coupling constant g
of the Higgs-Yukawa model, in the RPA mean-field approximation, for three decay
channels of the Higgs boson. Finally, we verify that, within our
approximations, only Higgs bosons with masses larger than 190 GeV/c^2 can decay
into top quarks.
