The non-relativistic limit of (central-extended) Poincare group and some consequences for quantum actualization

The nonrelativistic limit of the centrally extended Poincar\'e group is considered and their consequences in the modal Hamiltonian interpretation of quantum mechanics are discussed [ O. Lombardi and M. Castagnino, Stud. Hist. Philos. Mod. Phys 39, 380 (2008) ; J. Phys, Conf. Ser. 128, 012014 (2008) ]. Through the assumption that in quantum field theory the Casimir operators of the Poincar\'e group actualize, the nonrelativistic limit of the latter group yields to the actualization of the Casimir operators of the Galilei group, which is in agreement with the actualization rule of previous versions of modal Hamiltonian interpretation [ Ardenghi et al., Found. Phys. (submitted) ]