UV-IR Mixing in Non-Commutative Plane

Poincaré-invariant quantum field theories can be formulated on non-commutative planes if the coproduct on the Poincaré group is suitably deformed [1, 2].(See also especially Oeckl [3],[4] and Grosse et al.[5]) As shown in [6], this important result of these authors implies modification of free field commutation and anti-commutation relations and striking phenomenological consequences such as violations of Pauli principle [6, 7]. In this paper 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 [4]. E-mails: [email protected], [email protected], [email protected]