Primitively divergent diagrams in $\kappa$-deformed scalar field with quartic self-interaction

Abstract

We obtain the primitively divergent diagrams in $\kappa$-deformed scalar field in four-dimensional spacetime with quartic self-interaction in order to investigate the effect of the fundamental length $q=1/(2\kappa )$ on such diagrams. Thanks to $\kappa$-deformation, we find that the dimensionally regularized forms of the diagrams lead to finite results in the limit of space-time dimension four. The effect of the deformation appears as a displacement of the poles in the complex plane.

References in corpus (12)

• Modern tests of Lorentz invariance
• Lorentz violation at high energy: concepts, phenomena and astrophysical constraints
• Fock space, quantum fields and kappa-Poincaré symmetries
• Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
• From noncommutative kappa-Minkowski to Minkowski space-time
• Symplectic geometry and Noether charges for Hopf algebra space-time symmetries
• Scalar field theory on $\kappa$-Minkowski space-time and Doubly Special Relativity
• Field theory on kappa-spacetime
• Differential structure on the $\kappa$-Minkowski spacetime from twist
• $\kappa -$Minkowski spacetime and a uniformly accelerating observer
• Blackbody radiation in κ-Minkowski spacetime
• Effective action in DSR1 quantum field theory