The \(\beta\)-function in duality-covariant non-commutative \(\phi^4\)-theory

  • H. GrosseEmail author
  • R. Wulkenhaar
theoretical physics


We compute the one-loop \(\beta\)-functions describing the renormalisation of the coupling constant \(\lambda\) and the frequency parameter \(\Omega\) for the real four-dimensional duality-covariant non-commutative \(\phi^4\)-model, which is renormalisable to all orders. The contribution from the one-loop four-point function is reduced by the one-loop wavefunction renormalisation, but the \(\beta_\lambda\)-function remains non-negative. Both \(\beta_\lambda\) and \(\beta_\Omega\) vanish at the one-loop level for the duality-invariant model characterised by \(\Omega = 1\). Moreover, \(\beta_\Omega\) also vanishes in the limit \(\Omega\to 0\), which defines the standard non-commutative \(\phi^4\)-quantum field theory. Thus, the limit \(\Omega\to 0\) exists at least at the one-loop level.


Field Theory Quantum Field Theory Frequency Parameter Wavefunction Renormalisation 
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Copyright information

© Springer-Verlag Berlin/Heidelberg 2004

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität WienWienAustria
  2. 2.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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