Loop Calculations for the Non-Commutative U(1) Gauge Field Model with Oscillator Term

Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U(1) gauge field theory including an oscillator-like term in the action has been put forward in arXiv:0705.4205. The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed.