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UV-IR Mixing in Non-Commutative Plane

A. P. Balachandran·A. Pinzul·B. Qureshi
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Abstract

Poincaré-invariant quantum field theories can be formulated on non-commutative planes if the coproduct on the Poincaré group is suitably deformed \cite{Dimitrijevic:2004rf, Chaichian:2004za}.(See also especially Oeckl \cite{Oeckl:1999jun},\cite{Oeckl:2000mar} and Grosse et al.\cite{Grosse:2001mar}) As shown in \cite{Balachandran:2005eb}, 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 \cite{Balachandran:2005eb,Bal3}. 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 \cite{Oeckl:2000mar}.

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A. P. Balachandran, A. Pinzul, B. Qureshi. 2005-10-28. UV-IR Mixing in Non-Commutative Plane. https://doi.org/10.1016/j.physletb.2006.02.006

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