The noncommutative U(1) Higgs-Kibble model in the enveloping-algebra formalism and its renormalizability

Abstract

We discuss the renormalizability of the noncommutative U(1)Higgs-Kibble model formulated within the enveloping-algebra approach. We consider both the phase of the model with unbroken gauge symmetry and the phase with spontaneously broken gauge symmetry. We show that against all odds the gauge sector of the model is always one-loop renormalizable at first order in theta^{mu nu}, perhaps, hinting at the existence of a new symmetry of the gauge sector of the model. However, we also show that the matter sector of the model is non-renormalizable whatever the phase.

26 pages. Figures

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• Gauge theories on quantum spaces
• Massive Neutrino in Non-commutative Space-time
• Chiral fermions in noncommutative electrodynamics: renormalizability and dispersion
• Renormalisability of the matter determinants in noncommutative gauge theory in the enveloping-algebra formalism
• Noncommutative GUT inspired theories and the UV finiteness of the fermionic four point functions
• Bounds on the Parameter of Noncommutativity from Supernova SN1987A
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• Renormalisability of noncommutative GUT inspired field theories with anomaly safe groups
• Lorentz Violation in the Higgs Sector and Noncommutative Standard Model
• Hydrogen and muonic-Hydrogen Atomic Spectra in Non-commutative Space-Time
• Singlet particles as cold dark matter in noncommutative space-time
• Remarks on the 2nd order Seiberg-Witten maps
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• Noncommutative GUT inspired theories with U(1), SU(N) groups and their renormalisability
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences
• Higgs Couplings in NonCommutative Standard Model
• Noncommutative QED+QCD and $\beta$-function for QED
• Enveloping algebra Noncommutative SM: Renormalisability and High Energy Physics Phenomenology
• One-loop $\beta$ function of noncommutative scalar $QE{D}_4$
• Three-dimensional noncommutative Yukawa theory: Induced effective action and propagating modes