Self-consistent approximations for description of hadron gas at low-density

We study strongly interacting spin-isospin symmetric nuclear matter consisted of pions, nucleons and isobars at low baryon density and finite temperature T. Φ-functional of Baym is employed for the case of sandwich-like NNN diagrams. We explicitly showed coincidence of the zero component of Noether current and the one calculated by taking derivative of the thermodynamic potential over the baryon chemical potential μ_B. On example of N sandwich diagram of Φ we demonstrated equivalence of results obtained with the help of the Φ-functional of Baym and those found in the virial Beth-Uhlenbeck expansion performed up to the second order in exp(μ_B/T)