Non-renormalizability of θ-expanded noncommutative QED

Abstract

Computing all divergent one-loop Green's functions of θ-expanded noncommutative quantum electrodynamics up to first order in θ, we show that this model is not renormalizable. The reason is a divergence in the electron four-point function which cannot be removed by field redefinitions. Ignoring this problem, we find however clear hints for new symmetries in massless θ-expanded noncommutative QED: Four additional divergences which would be compatible with gauge and Lorentz symmetries and which are not reachable by field redefinitions are absent.

30 pages, LaTeX, JHEP.cls, uses the feynmf package to draw 96 Feynman graphs. v2: minor corrections, references added, adapted to JHEP style

References in corpus (7)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• Introduction to M(atrix) theory and noncommutative geometry, Part II
• Algebras of distributions suitable for phase-space quantum mechanics. I
• Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map
• Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map
• Generalized Yang-Mills actions from Dirac operator determinants

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