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

We obtain the primitively divergent diagrams in $κ$-deformed scalar field in four-dimensional spacetime with quartic self-interaction in order to investigate the effect of the fundamental length $q=1/(2κ)$ on such diagrams. Thanks to $κ$-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.

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