Noncommutative field with constant background fields and neutral fermion

Introducing constant background fields into the noncommutative gauge theory, we first obtain a Hermitian fermion Lagrangian which involves a Lorentz violation term, then we generalize it to a new deformed canonical noncommutation relations for fermion field. Massless neutrino oscillation in the deformed canonical noncommutation relations is analyzed. The restriction of the noncommutative coefficients is also discussed. By comparing with the existing experimental data of conventional neutrino oscillations, the order of noncommutative deformed coefficients is given from different ways.