On the tensor vs. the vector character of the director field in a nematic liquid crystal

Abstract

The description of the director field of the nematic phase of a liquid crystalline material is investigated. It is shown that utilizing a tensor field to represent the director has exactly the same physical consequences as the more commonly used vector field. Furthermore it is proven that a nematic tensor field can always be replaced by the square of a vector field for which the Frank-Oseen expression holds.