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We clearly show that the symplectic structures deformations lead, uponquantization, to quantum theories of non commutative fields. Two variants ofdeformations are considered. The quantization is performed and the modesexpansions of the quantum fields are derived. The Hamiltonians are given andthe degeneracies lifting induced by the deformation is also discussed. Asillustration, we consider the noncommutative chiral boson fields in the contextof fractional quantum Hall effect. A generalized fractional filling factor isderived and shown to reproduce the Jain Hall states. We also show that thecoupling of left and right edge excitations of a quantum Hall sample, givesrise a noncommutative chiral boson theory. The coupling or thenon-commutativity induces a shift of the chiral components velocities. A nonlinear dispersion relation is obtained corroborating some recent analytical andnumerical analysis.

Symplectic Deformations, Non Commutative Scalar Fields and Fractional Quantum Hall Effect