Classification of the collectice modes of the order parameter in superfluid 3He

The collective modes in the A-phase of superfluid 3He are classified with respect to the irreducible representations of the ''vacuum'' H symmetry group. In contrast to the modes in 3He-B, which are characterized by a single quantum number J and a single parity (with respect to complex conjugation), the modes in 3He-A are characterized by two quaptum numbers Q and Ssub(z) with two parities P1 and P2. The charges Q and Ssub(z) assume the values 0, +-1, +-2 and 0+ +-1 respectively. Due to the parities P1 and P2+ those modes which differ in the sign of Ssub(z) or sign of Q turn out to be degenerate. Consequently, if the wave vector q is parallel to the orbital anisotropy axis there will be two four-fold degenerate branches in the mode spectrum, 4 two-fold degenerate and 2 non-degenerate. The splitting of the mode spectrum on lowering of vacuum H symmetry due to spin-orbit coupling and to the magnetic field is investigated. It is shown that additional degeneracy of the mode spectrum occurs in the weak coupling limit at the expense of expansion of the H group due to the hidden symmetry. The consequences of asymmetry between quasiparticles and holes near the Fermi surface, which results in a splitting of the spectrum of modes with different signs