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

TL;DR

This paper explores how the nonrelativistic limit of the centrally extended Poincaré group influences the actualization of Casimir operators, impacting the modal Hamiltonian interpretation of quantum mechanics.

Contribution

It demonstrates that the nonrelativistic limit leads to the actualization of Galilei group Casimir operators, linking relativistic and nonrelativistic quantum interpretations.

Findings

Casimir operators of Poincaré group actualize in quantum field theory

Nonrelativistic limit yields Casimir operators of Galilei group

Supports previous modal Hamiltonian interpretation rules

Abstract

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) ]