Integrability and volume-preserving diffeomorphisms
Abstract:
We construct a class of field theories which are either integrable
or contain integrable subsectors defined by additional constraints. Here
integrability means the existence of infinitely many conservation laws.
These theories have three-dimensional target space, like the Skyrme model,
and their infinitely many conserved currents turn out to be Noether
currents of the volume-preserving diffeomorphisms on target space.
Further, we discuss applications to some specific field theories.