Field theory on $\kappa$--Minkowski space revisited: Noether charges and breaking of Lorentz symmetry

Understand

This paper is devoted to detailed investigations of free scalar field theory on $\kappa$-Minkowski space.

• After reviewing necessary mathematical tools we discuss in depth the Lagrangian and solutions of field equations.
• We analyze the spacetime symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetry.
• We show that the version of the theory usually studied breaks Lorentz invariance in a subtle way: There is an additional trans-Planckian mode present, and an associated conserved charge (the number of such modes) is not a Lorentz scalar.