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Translation invariance, commutation relations and ultraviolet/infrared mixing

2009/07/21 by Salvatore Galluccio, Fedele Lizzi, Patrizia Vitale
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1088/1126-6708/2009/09/054

published as JHEP 0909:054,2009 · 24 pages, 1 figure

arxiv created 2009/07/21 · openalex publication_date 2009/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations