Remarks on exactly solvable noncommutative quantum field

We study exactly the solvable noncommutative scalar quantum held models of (2n) or (2n + 1) dimensions. By writing out an equivalent action of the noncommutative held, it is shown that the special condition B . theta = +/- I in held theoretic context means the full restoration of the maximal U(infinity) gauge symmetries broken due to kinetic term. It is further shown that the model can be obtained by dimensional reduction of a 2n-dimensional exactly solvable noncommutative phi(4) quantum held model closely related to the 1+1-dimensional Moyal/matrix-valued nonlinear Schrodinger (MNLS) equation. The corresponding quantum fundamental commutation relation of the MNLS model is also given explicitly.