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Light-like $κ$-deformations and scalar field theory via Drinfeld twist

In this article we will use the Drinfeld twist leading to light-like $κ$-deformations of Poincaré algebra. We shall apply the standard Hopf algebra methods in order to define the star-product, which shall be used to formulate a scalar field theory compatible with $κ$-Poincaré-Hopf algebra. Using this approach we show that there is no problem with formulating integration on $κ$-Minkowski space and no need for introducing a new measure. We have shown that the $\star$-product obtained from this twist enables us to define a free scalar field theory on $κ$-Minkowski space that is equivalent to a commutative one on a usual Minkowski space. We also discuss the interacting $ϕ^4$ scalar field model compatible with $κ$-Poincaré-Hopf algebra.