Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-02-07
Mod.Phys.Lett.A24:1721-1730,2009
Physics
High Energy Physics
High Energy Physics - Theory
12 pages
Scientific paper
10.1142/S0217732309031156
The Moyal and Wick-Voros planes A^{M,V}_{\theta} are *-isomorphic. On each of these planes the Poincar\'e group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors. We show that the *-isomorphism T: A^M_{\theta} to A^V_{\theta} does not also map the corresponding twists of the Poincar\'e group algebra. The quantum field theories on these planes with twisted Poincar\'e-Hopf symmetries are thus inequivalent. We explicitly verify this result by showing that a non-trivial dependence on the non-commutative 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). Our results differ from these of (arXiv:0810.2095 [hep-th]) because of differences in the treatments of quantum field theories.
Balachandran Aiyalam P.
Martone Mario
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