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We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalizedat the one-loop level by multiplicative dimensional renormalization of thecoupling constant and fields of the theory. We compute the beta function of thetheory and conclude that the theory is asymptotically free. We also show thatthe Weyl-Moyal matrix defining the deformed product over the space of functionson R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and  the divergent contributions corrected accordingly. As a result the model  turns out to be asymptotically fre

physical review letters

One-Loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ℝ</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi /></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>

One-Loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutativeℝ4