UV-IR Mixing in Non-Commutative Plane

TL;DR

This paper demonstrates that in Poincaré-invariant quantum field theories on non-commutative planes, UV-IR mixing is eliminated at all orders in perturbation theory due to modified commutation relations.

Contribution

The authors prove that UV-IR mixing vanishes to all orders in perturbation theory in non-commutative quantum field theories with deformed Poincaré symmetry.

Findings

UV-IR mixing is absent at all perturbation orders.

Modified commutation relations lead to phenomenological consequences.

Results align with previous findings by Oeckl.

Abstract

Poincar\'e-invariant quantum field theories can be formulated on non-commutative planes if the coproduct on the Poincar\'e 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}.