Clebsch (String) Parameterization of 3-Vectors and Their Actions
  We discuss some properties of the intrinsically nonlinear Clebsch decomposition of a vector field into three scalars in d=3. In particular, we note and account for the incompleteness of this parameterization when attempting to use it in variational principles involving Maxwell and Chern-Simons actions. Similarities with string decomposition of metrics and their actions are also pointed out. 
S. Deser, R. Jackiw, A.P. Polychronakos