Elementary excitations of a relativistic scalar plasma system

In a previous work [1] we have presented a framework to investigate the initial-value problem in the context of interacting fermion-scalar field theories. The method allows one to obtain a set of self-consistent equations for the expectation values of the linear and bilinear forms of field operators. These dynamical equations acquire the structure of the kinetic type, where the lowest order of the approximation corresponds to the usual gaussian mean-field approximation (collisionless). In [1], as an application, we have implemented a zero-order calculation within the simplest context of relativistic scalar plasma system. We have shown that the usual prescription of renormalization can also be applied to this non-perturbative calculation. In particular, we have obtained a finite expression for the energy density and the numerical results suggested that the system presents always a single stable minimum. In continuation of [1] we report a particular application of the renormalized nonlinear dynamics obtained in the previous publication. In this work [2] we investigate the physics of elementary excitations of the relativistic scalar plasma system. Following the standard many-body procedure to investigate the near equilibrium dynamics, we have obtained the RPA equations for this model by linearizing the TDHF equations of motion around the stationary solution obtained in [1]. The resulting equations have a closed solution, from which one can examine the spectrum of elementary excitation modes of the relativistic scalar plasma model. We show that the amplitudes of these oscillation modes can be identified with quantum particles, more specifically with one-meson and two-fermion state of the theory. In particular, our results indicate existence of bound state for certain region of phase diagram. (author)