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

TL;DR

This paper derives an explicit star product for the $kappa$-Minkowski Lie algebra in any dimension, using symplectic realization and reduction of the Wick-Voros product, connecting it to a Jordanian twist.

Contribution

It provides a new explicit expression for the $kappa$-Minkowski star product in arbitrary dimensions via symplectic reduction and twist methods.

Findings

Explicit star product formula for $kappa$-Minkowski in any dimension

Connection established between star product and Jordanian twist

Reduction of Wick-Voros product to $kappa$-Minkowski case

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.