Decomposition of Noncommutative U(1) Gauge Potential

We investigate the decomposition of noncommutative gauge potentialÂ_i, and find that it has inner structure, namely,Â_i can be decomposed in two parts, hat{b}_i andâ_i, where hat{b}_i satisfies gauge transformationswhile â_i satisfies adjoint transformations, so dose theSeiberg-Witten mapping of noncommutative U(1) gauge potential. Bymeans of Seiberg-Witten mapping, we construct a mapping of unitvector field between noncommutative space and ordinary space, andfind the noncommutative U(1) gauge potential and its gauge fieldtensor can be expressed in terms of the unit vector field. When theunit vector field has no singularity point, noncommutative gaugepotential and gauge field tensor will equal ordinary gaugepotential and gauge field tensor