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One-loop beta functions for the orientable non-commutative Gross-Neveu model. (English) Zbl 1189.81219

Summary: We compute at the one-loop order the \(\beta \)-functions for a renormalisable non-commutative analog of the Gross-Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The \(\beta \)-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.

MSC:

81T75 Noncommutative geometry methods in quantum field theory
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