Hydrodynamics of Nuclear Matter in the Chiral Limit

Using the Poisson bracket method, we construct the hydrodynamics of nuclear matter in the chiral limit, which describes the dynamics of all low-energy degrees of freedom, including the fluid-dynamical and pionic ones. The hydrodynamic equations contain, beside five Euler equations of relativistic fluid dynamics, $N_{\mathrm{f}}^2-1\mathrm{}$ second order equations describing propagating pions and $N_{\mathrm{f}}^2-1\mathrm{}$ first order equations describing the advection of the vector isospin charges. We present hydrodynamic arguments showing that the pion velocity vanishes at the second order phase transition at $N_{\mathrm{f}}=2\mathrm{}$.