We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-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.
Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing / Galluccio, Salvatore; Lizzi, Fedele; Vitale, Patrizia. - In: JOURNAL OF HIGH ENERGY PHYSICS. - ISSN 1029-8479. - ELETTRONICO. - 2009:(2009), p. 054. [10.1088/1126-6708/2009/09/054]
Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing.
GALLUCCIO, salvatore;LIZZI, FEDELE;VITALE, PATRIZIA
2009
Abstract
We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.