The Theory of Quantum Fermi-Liquid Solutions with a Vector Order Parameter

We construct the thermodynamic theory and derive the hydrodynamic equations for a solution of Fermi superfluids with a vector order parameter. The thermodynamic quantities related to spontaneous breaking of phase symmetries and spin rotations are represented in terms of the order-parameter operator. We predict a new entrainment effect related to the mutual influence of magnetic and orbital degrees of freedom. We find the spectra of collective excitations and discuss the distinctions between the states under consideration and those with scalar and vector order parameters.