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We provide a new approach to study the noncommutative effects on the neutralDirac particle with anomalous magnetic or electric dipole moment on thenoncommutative plane. The advantages of this approach are demonstrated byinvestigating the noncommutative corrections on the Aharonov-Casher andHe-McKellar-Wilkens effects. This approach is based on the effective $U(1)$gauge symmetry for the electrodynamics of spin on the two dimensional space.The Seiberg-Witten map for this symmetry is then employed when we study thenoncommutative corrections. Because the Seiberg-Witten map preserves the gaugesymmetry, the noncommutative corrections can be defined consistently with theordinary phases. Based on this approach we find the noncommutative correctionson the Aharonov-Casher and He-McKellar-Wilkens phases consist of two terms. Thefirst one depends on the beam particle velocity and consistence with theprevious results. However the second term is velocity-independent and thencompletely new. Therefore our results indicate it is possible to investigatethe noncommutative space by using ultra-cold neutron interferometer in whichthe velocity-dependent term is negligible. Furthermore, both these two termsare proportional to the ratio between the noncommutative parameter $\theta$ andthe cross section $A_{e/m}$ of the electrical/magnetic charged line enclosed bythe trajectory of beam particles. Therefore the experimental sensitivity can besignificantly enhanced by reduce the cross section of the charge line$A_{e/m}$.

Seiberg-Witten map and quantum phase effects for neutral Dirac particle on noncommutatiave plane