COLLECTIVE EXCITATIONS IN THE 2D PLANAR PHASE OF SUPERFLUID HE-3

For the first time the complete spectrum of collective excitations in the 2D planar phase of superfluid He-3 is calculated. In order to calculate the spectrum, the path integration method developed by Brusov and Popov [1] is used. The spectrum contains the modes known before from the A-phase spectrum [2] (i.e. goldstone, clapping and pair-breaking), as well as the new modes existing only in the 2D phase [3]. Noteworthy is that the frequencies of clapping and pair-breaking modes exhibiting the linear Zeeman effect in the A-phase are independent of magnetic field in the 2D phase. The collective mode energies are complex, what is associated with vanishing the gap in the single-particle spectrum along the fixed direction, on the analogy to the case of the A-phase.