Noncommutative QED+QCD and $\beta$-function for QED

Abstract

QED based on $\theta$-unexpanded noncomutative space-time in contrast with the noncommutative QED based on $\theta$-expanded U(1) gauge theory via the Seiberg-Witten map, is one-loop renormalizable. Meanwhile it suffers from asymptotic freedom that is not in agreement with the experiment. We show that QED part of $U_{\star }(3)\times U_{\star }(1)$ gauge group as an appropriate gauge group for the noncommutative QED+QCD, is not only one-loop renormalizable but also has a $\beta$ function that can be positive, negative and even zero. In fact the $\beta$ function depends on the mixing parameter ${\delta }_{13}$ as a free parameter and it will be equal to its counterpart in the ordinary QED for ${\delta }_{13}=0.367\pi$.

33 pages, 30 figures, to appear in PRD

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Cited by in corpus (4)

• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Higgs Couplings in NonCommutative Standard Model
• Lorentz violation parameters and noncommutative scale
• Nucleon structure functions in noncommutative space-time