Lorentz invariance of scalar field action on $\kappa$-Minkowski space-time

TL;DR

This paper develops a Lorentz-invariant scalar field theory on noncommutative $$-Minkowski space-time, demonstrating invariance of the Lagrangian and adapting calculus rules to noncommutative geometry.

Contribution

It constructs a Lorentz-invariant scalar field theory on $$-Minkowski space-time, introducing a coproduct-based calculus to handle noncommutativity.

Findings

Field Lagrangian is Lorentz invariant on noncommutative space

Noncommutativity necessitates replacing Leibnitz rule with coproduct

The framework maintains Lorentz symmetry in noncommutative setting

Abstract

We construct field theory on noncommutative $\kappa$-Minkowski space-time. Having the Lorentz action on the noncommutative space-time coordinates we show that the field lagrangian is invariant. We show that noncommutativity requires replacing the Leibnitz rule with the coproduct one.