UV–IR mixing in non-commutative plane

Abstract

Poincaré-invariant quantum field theories can be formulated on non-commutative planes if the coproduct on the Poincaré group is suitably deformed. As shown in our previous work, this important result implies modification of free field commutation and anti-commutation relations and striking phenomenological consequences such as violations of Pauli principle. In this Letter we prove that with these modifications, UV–IR mixing disappears to all orders in perturbation theory from the S-matrix. This result is in agreement with the previous results of Oeckl.