We propose a model for a relativistic many-body system at finite temperature in the framework of thermo field dynamics, which is a real-time formalism of finite-temperature field theory. Our model contains the scalar (σ) and the vector (ω) mesons as well as the Dirac nucleon. The full propagator and self-energy for each particle are presented in terms of spectral representations. The Feynman rules for a perturbation expansion are shown. They are applied to the study of collective modes in hot and dense matter within the random-phase approximation. The dispersion relations of the longitudinal and transverse collective modes in the meson branch are calculated. We also estimate the effective meson mass which is defined as the energy needed to create one meson at rest in extreme matter. The effects of vacuum fluctuations are also examined. They contribute a fair amount to the collective modes through the effective nucleon mass.

• Received 13 February 1989

DOI:https://doi.org/10.1103/PhysRevC.40.407