We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeros of associated transfer matrix eigenvalues with the exact results of the ferromagnetic three-state Potts chain and the three-state superintegrable chiral Potts model. We find that the spectrum is described in terms of quasi-particles with momenta restricted only to segments of the Brillouin zone 0≤P≤2π where the boundaries of the segments depend on the chiral angles of the model.
We discuss field-theoretical foundations of Landau's quasi-particle concept for strongly interacting Bosons.The historical development starting from Belyaev's field theory up to modern renormalization group theory is briefly reviewed with a particular emphasis on the problem of infrared divergences.It is shown in detail that the correlation functions obtained in Popov's functional integral approach based on a hydrodynamic action agrees precisely with recent renormalization group analysis.The phonon decay is also discussed.