Distortional Lifshitz Vectors and Helicity in Nematic Free Energy   Density
  Here we discuss the free energy of nematic liquid crystals using two vectors and the helicity, with the aim of having a compact form of its density. The two vectors are due to the splay and bend distortions of the director field. They have a polar nature, whereas the helicity is a pseudoscalar. 
Amelia Carolina Sparavigna
cond-mat.soft physics.pop-ph