Interacting scalar field theory in $\kappa$-Minkowski spacetime

TL;DR

This paper develops a complex scalar field theory in $kappa$-Minkowski spacetime that maintains $kappa$-deformed Poincaré symmetry, demonstrating finiteness at one-loop and revealing unique imaginary corrections from complex poles.

Contribution

It introduces a novel scalar field theory in $kappa$-Minkowski spacetime that respects deformed symmetry and analyzes its quantum properties.

Findings

The theory is finite at one-loop level.

Finite renormalization is required for the $kappa o bb{R}$ limit.

The loop correction includes an imaginary component due to complex poles.

Abstract

We construct an complex scalar field theory in $\kappa$-Minkowksi spacetime, which respects $\kappa$-deformed Poincar\'e symmetry. One-loop calculation shows that the theory is finite and needs finite renormalization to be compatible with the $\kappa \to \infty$ limit. The loop result also has an imaginary valued correction due to the complex poles present in the propagator.