Translation invariance, commutation relations and ultraviolet/infrared mixing

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Published 9 September 2009 Published under licence by IOP Publishing Ltd
, , Citation Salvatore Galluccio et al JHEP09(2009)054 DOI 10.1088/1126-6708/2009/09/054

1126-6708/2009/09/054

Abstract

We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Grönewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic feature of translationally invariant associative products. We find, with an explicit calculation that the phase appearing in the nonplanar diagrams is the one given by the commutator of the coordinates, the semiclassical Poisson structure of the non commutative spacetime. We do this with an explicit calculation for represented generic products.

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10.1088/1126-6708/2009/09/054