Séminaire Poincare ́ X (2007) 15 – 95 Séminaire Poincaré

Abstract. A new version of scale analysis and renormalization theory has been found on the non-commutative Moyal space. It could be useful for physics beyond the standard model or for standard physics in strong external field. The good news is that quantum field theory is better behaved on non-commutative than on ordinary space: indeed it has no Landau ghost. We review this rapidly growing subject.