On the consistency of DSR models for multiparticle systems

The aim of the thesis is to provide a new original solution proposal to the infamous soccer-ball problem in the k-Poincaré inspired DSR (Doubly or Deformed Special Relativity) theory. More specifically, through the analysis of the kinematical properties of a composite system, we show that the single-particle deformation effects typical of the k-Poincaré setup should become weaker and weaker as the number of particles composing the system grows higher. After proposing a consistent definition of the "total" symmetry algebra of this system, we explore the so-called k-galilean limit of the theory. In particular, by avoiding the special relativistic no-interaction theorem, we are able to perform a first analysis of the quantum mechanical properties of an interacting two-particle system in the non-commutative k-Poincaré framework.