2009/02/28 by A. P. Balachandran, A. P. BALACHANDRAN, M. Martone +1 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1142/s0217732309031156
published as Mod.Phys.Lett.A24:1721-1730,2009 · 12 pages
arxiv created 2009/04/12 · openalex publication_date 2009/07/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The Moyal and Wick–Voros planes [Formula: see text] are *-isomorphic. On each of these planes the Poincaré group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors [Formula: see text]. We show that the *-isomorphism [Formula: see text] also does not map the corresponding twists of the Poincaré group algebra. The quantum field theories on these planes with twisted Poincaré–Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a nontrivial dependence on the noncommutative parameter is present for the Wick–Voros plane in a self-energy diagram whereas it is known to be absent on the Moyal plane (in the absence of gauge fields). 1–3 Our results differ from those of Ref. 4 because of differences in the treatments of quantum field theories.