arXiv 0902.12472009-02hep-thgr-qcmath-phmath.MPmath.QA

Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent

A. P. Balachandran, M. Martone

备注：: 12 pages
发表信息：: Mod.Phys.Lett.A24:1721-1730,2009
DOI：: 10.1142/S0217732309031156

英文摘要：

The Moyal and Wick-Voros planes A^{M,V}_θ are *-isomorphic. On each of these planes the Poincaré group acts as a Hopf algebra symmetry if its coproducts are deformed by twist factors. We show that the *-isomorphism T: A^M_θ to A^V_θ does not also 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 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.

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