Quantization Rules for Point Singularities in SuperfluidHe3and Liquid Crystals

Abstract

I show that pointlike singularities can exist in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Integer quantum numbers are associated with these singularities. The quantization rules follow from the single valuedness of the order parameter and quantities derived from it. The results are also easily extended to the quantization of point singularities in nematic liquid crystals. The pointlike singularities in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ are experimentally accessible analogs of the magnetic monopole.