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

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, 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 antiparticles are the output of the minimization of the thermodynamical potential. It is shown that in the mean field theory the thermodynamical consistency is achieved. The connection with effective chiral lagrangians with Brown-Rho scaling is discussed.