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Clebsch (string) decomposition in $$d=3$$ field theory. (English) Zbl 0972.81198
Summary: We study the applicability of the intrinsically nonlinear Clebsch vector field decomposition into three scalars in the description of $$d=3$$ field theories. 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.

##### MSC:
 81T99 Quantum field theory; related classical field theories
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