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Duality and gauge invariance of noncommutative spacetime Podolsky electromagnetic theory

The interest in higher derivatives field theories has its origin mainly in their influence concerning the renormalization properties of physical models and to remove ultraviolet divergences. In this letter we have introduced the noncommutative (NC) version of the Podolsky theory and we investigated the effect of the noncommutativity over its original gauge invariance property. We have demonstrated precisely that the noncommutativity spoiled the gauge invariance of the original action. After that we have used the Noether dualization technique to obtain a dual and gauge invariant action. More than to obtain the NC Podolsky theory, we have another motivation in this work, which is to show that, although the introduction of noncommutativity spoils the gauge invariance, it is possible to recover this property using a standard dualization method which did not need any modification due to any NC effect in the original theory, by the way