Abstract
We study the non-commutative gauge theory on the Moyal space. We add the harmonic potential introduced by Grosse and Wulkenhaar to the Maxwell Lagrange as well as the Gauge fixation. We determine the non-commutative U*(1) Gauge action which is invariant under the BRST transformations in the matrix basis. We determine in this basis the quadratic parts and the vertex of the Gauge field Aμ and of the Faddeev-Popov ghost fields c̄andc. Finally, we study the perturbative correction to one loop order of the one point function in the matrix basis.
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