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Particles and Fields
Eur. Phys. J. C 32, 269-280 (2004)
DOI: 10.1140/epjc/s2003-01396-8

No UV/IR mixing in unitary space-time non-commutative field theory

P. Fischer1 and V. Putz2

1  Theory Division, CERN, 1211 Geneva 23, Switzerland
2  Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany

pfischer@mail.cern.ch
putz@hep.itp.tuwien.ac.at

(Received: 26 August 2003 / / Published online: 20 November 2003)

Abstract
In this article we calculate several divergent amplitudes in $\phi^4$-theory on non-commutative space-time ( $\Theta_{0i} \neq 0$) in the framework of interaction-point time-ordered perturbation theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules that allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the absence of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in general. Together with the Feynman rules we found, this opens promising vistas onto the systematic renormalization of non-commutative field theories.



© Società Italiana di Fisica, Springer-Verlag 2004