Chiral dynamics of nuclear matter at finite temperature

We extend a recent three-loop calculation of nuclear matter in the systematic framework of chiral perturbation theory to finite temperatures T. The contributions from one- and two-pion exchange diagrams which cause nuclear binding and saturation at T=0 are included for T>0 in the density and temperature dependent free energy per particle, $\bar F(rho,T)$. The so-called anomalous 2pi-exchange contribution $\bar A(rho,T)$ (with no counterpart in the ground state energy density at T=0) is consistently included. The calculated pressure isotherms display the familiar first-order liquid-gas phase transition of isospin symmetric nuclear matter with a critical point at T_c = 25.5 MeV and rho_c = 0.09 fm^{-3}. The too high value of the critical temperature originates from the strong momentum dependence of the underlying single-particle potential U(p,k_{f0}) near the Fermi-surface. We also consider pure neutron matter at T>0 in the same framework and find fair agreement with sophisticated many-body calculations for neutron densities rho_n < 0.2 fm^{-3}.