Field theory on κ-minkowski space revisited:: Noether charges and breaking of lorentz symmetry

This paper is devoted to detailed investigations of free scalar field theory on kappa-Minkowski space. After reviewing necessary mathematical tools, we discuss in detail the Lagrangian and solutions of field equations. We analyze the space-time symmetries of the model and construct the conserved charges associated with translational and Lorentz symmetries. 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.