  The two-dimensional ideal (Euler) fluids can be described by the classical
fields of streamfunction, velocity and vorticity and, in an equivalent manner,
by a model of discrete point-like vortices interacting in plane by a
self-generated long-range potential. This latter model can be formalized, in
the continuum limit, as a field theory of scalar matter in interaction with a
gauge field, in the $su(2) $ algebra. This description has already offered the
analytical derivation of the \emph{sinh}-Poisson equation, which was known to
govern the stationary coherent structures reached by the Euler fluid at
relaxation. In order this formalism to become a familiar theoretical instrument
it is necessary to have a better understanding of the physical meaning of the
variables and of the operations used by the field theory. Several problems will
be investigated below in this respect.
