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

Understand

In this article we will use the Drinfeld twist leading to light-like $\kappa$-deformations of Poincar\'e 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 $\kappa$-Poincar\'e-Hopf algebra.
• Using this approach we show that there is no problem with formulating integration on $\kappa$-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 $\kappa$-Minkowski space that is equivalent to a commutative one on a usual Minkowski space.