On the density-dependent hadron field theory at finite temperature and its thermodynamical consistency

Abstract

In this work we study in a formal way the density-dependent hadron field theory at finite temperature for nuclear matter. The thermodynamical potential and related quantities, such as energy density and pressure, are derived in two different ways. We first obtain the thermodynamical potential from the grand partition function, where the Hamiltonian depends on the density operator and is truncated at first order. We then reobtain the thermodynamical potential by calculating explicitly the energy density in a Thomas–Fermi approximation and considering the entropy of a Fermi gas. The distribution functions for particles and anti-particles are the output of the minimization of the thermodynamical potential. It is shown that in the mean field theory thermodynamical consistency is achieved. The connection with effective chiral Lagrangians having Brown–Rho scaling is discussed.