Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing

Details Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing Translation Invariance, Commutation Relations and Ultraviolet/Infrared Mixing

2009-07-21

arxiv.org/abs/0907.3640v1

JHEP 0909:054,2009

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 1 figure

Scientific paper

10.1088/1126-6708/2009/09/054

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.

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