Clebsch (String) Parameterization of 3-Vectors and Their Actions

Deser, S.; Jackiw, R.; Polychronakos, A. P.

Clebsch (String) Parameterization of 3-Vectors and Their Actions

Authors

Deser, S.

Jackiw, R.

Polychronakos, A. P.

Description

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.
4 pages, LaTeX; email correspondence to jackiw@mitlns.mit.edu