$\kappa$-Minkowski star product in any dimension from symplectic realization

Abstract

We derive an explicit expression for the star product reproducing the $\kappa$-Minkowski Lie algebra in any dimension $n$. The result is obtained by suitably reducing the Wick-Voros star product defined on $\mathbb{C}^{d}_\theta$ with $n=d+1$. It is thus shown that the new star product can be obtained from a Jordanian twist.