Fields and symmetries in $\kappa$-Minkowski noncommutative spacetime

Abstract

We have investigated some issues relevant for the possibility to construct physical theories on the $\kappa$-Minkowski noncommutative spacetime. The notion of field in $\kappa$-Minkowski has been introduced by generalizing the Weyl system/map formalism and a comparative study of the star products arising from this generalization has been done. A line of analysis of the symmetries of $\kappa$-Minkowski has been proposed that relies on the possibility to find a "maximally"-symmetric action which is invariant under a 10-generator Poincar\'e-like symmetry algebra. The equation of motion for scalar particles has been obtained by a generalized variational principle. An extension of the Dirac equation for spin-1/2 particles has been proposed by using a five-dimensional differential calculus on $\kappa$-Minkowski.