κ-Poincaré invariant orientable field theories at one-loop

  • Timothé Poulain
  • Jean-Christophe WalletEmail author
Open Access
Regular Article - Theoretical Physics


We consider a family of κ-Poincaré invariant scalar field theories on 4-d κ-Minkowski space with quartic orientable interaction, that is for which ϕ and its conjugate ϕ alternate in the quartic interaction, and whose kinetic operator is the square of a Uκ(iso(4))-equivariant Dirac operator. The formal commutative limit yields the standard complex ϕ4 theory. We find that the 2-point function receives UV linearly diverging 1-loop corrections while it stays free of IR singularities that would signal occurrence of UV/IR mixing. We find that all the 1-loop planar and non-planar contributions to the 4-point function are UV finite, stemming from the existence of the particular estimate for the propagator partly combined with its decay properties at large momenta, implying formally vanishing of the beta-functions at 1-loop so that the coupling constants stay scale-invariant at 1-loop.


Renormalization Regularization and Renormalons Models of Quantum Gravity Non-Commutative Geometry 


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© The Author(s) 2019

Authors and Affiliations

  1. 1.Laboratoire de Physique Théorique, CNRS and Université Paris-Sud 11Orsay CedexFrance

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