Classification of the Equilibrium States of $^{3}$He

Based on the concept of quasiaverages, we classify the equilibrium states of the superfluid $^{3}$He with due regard to possible inhomogeneous structures. We establish a relation of the residual and spatial symmetry conditions to a helicoidal ordering of the spatial anisotropy vector and a spiral structure of the magnetic anisotropy vector. We show that the set of anisotropic homogeneous equilibrium states can be classified in terms of two quantum numbers corresponding to the projections of the Cooper-pair spin and orbital momentum onto the anisotropy directions.