Fun from none: deformed symmetries and Fock space

We give a pedagogical introduction to the basics of deformations of relativistic symmetries and the Hilbert spaces of free quantum fields built as their representations. We focus in particular on the example of a $\kappa$-deformed scalar quantum field for which the generators of spatial translations that label the field modes act according to a deformed Leibnitz rule. We explore the richer structure of the $\kappa$-Fock space and point out possible physical consequences of the deformation.