Theory of orbital dynamics of the A phase of superfluid 3He. II. Orbital hydrodynamic equations

Orbital hydrodynamic equations in ³He-A are derived microscopically in the hydrodynamic regime near the transition temperature. Transport coefficients as well as reactive coefficients are evaluated as rigorously as possible. The expression for the time derivative of the phase of the order parameter is shown to contain l · rot _n with the Yosida function as a coefficient. It is shown that when the supercurrent is given by the usual definition which includes only the first-order space derivative of the order parameter, the stress tensor becomes antisymmetric and there is an additional contribution to the local angular momentum density of dynamical origin. The stress tensor can be made symmetric by changing the definition of the supercurrent.