  We clearly show that the symplectic structures deformations lead, upon
quantization, to quantum theories of non commutative fields. Two variants of
deformations are considered. The quantization is performed and the modes
expansions of the quantum fields are derived. The Hamiltonians are given and
the degeneracies lifting induced by the deformation is also discussed. As
illustration, we consider the noncommutative chiral boson fields in the context
of fractional quantum Hall effect. A generalized fractional filling factor is
derived and shown to reproduce the Jain Hall states. We also show that the
coupling of left and right edge excitations of a quantum Hall sample, gives
rise a noncommutative chiral boson theory. The coupling or the
non-commutativity induces a shift of the chiral components velocities. A non
linear dispersion relation is obtained corroborating some recent analytical and
numerical analysis.
