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

  • H. GrosseEmail author
  • R. Wulkenhaar
theoretical physics

Abstract.

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.

Keywords

Field Theory Quantum Field Theory Frequency Parameter Wavefunction Renormalisation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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