Relativistic Many-Body Theory for Strongly Interacting Matter

Abstract

The relativistic many-body theory for the equation of state describing a strongly interacting system of baryons in flat space-time is presented. After giving the coupled equation of motion for relativistic Green's functions, which include finite density and temperature as boundary conditions, we develop relativistic expressions for the pressure and the energy density of the interacting system in terms of the fermion two-point function. The latter is expressed by an integral equation, which includes the pseudoscalar coupling to lowest order in the coupling constant. The result is regularized, and renormalization to both physical and effective mass and charge is discussed. The expressions obtained serve as the basis for a numerical calculation of the equation of state which is presented in the following paper. A significant feature of our results is a fully relativistic equation of state which includes interactions, and which leads to an asymptotic limit for the speed of sound $v_s\le \frac{c}{\sqrt{3}}$.