The simplest classical observables originate from symmetry properties of a quantum system; three examples of such behavior are provided: the fermion / boson property, the mass of a "nonrelativistic" particle, and the particle number in Fock space.
We reinvestigate Bargmann's superselection rule for the overall mass of n particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an \\reals-extension of the Galilei group which formerly appeared only at the quantum level. There is now no obstruction to implement an action of the classical symmetry group on Hilbert space. We include some critical comments of a general nature on formal derivations of superselection rules without dynamical context.
We investigate the causes of the curious property of neutrino oscillations of looking as an interference between fully distinguishable particles. The sources of this effect are identified as to be determined by the many particle nature of space of states of the quantum field theory. It is firstly underlined that in order to explain the observed oscillations, the neutrino subspace of states should not be interpreted as the direct product of the three neutrinos Fock spaces, which is equivalent to imposing a superselection rule. Further, it is argued that the linear completion of such a direct product space of states permits to describe the measured oscillations. Thus, the space of states of te Standard Model (SM) should be interpreted as the linear completion of the direct product of all the Fock spaces (boson or fermions ones) associated to the distinguishable particles. Then, it follows that the neutrino oscillations are determined as interference between independent particles, which are generated by states being outside the direct product of the neutrino Fock spaces. This interpretation seems to imply a large amount of interference observations between distinguishable particles in Particle as well as in Condensed Matter Physics. For seeking clearness, the discussion is done in the framework of a simple Quantum Field Theory (QFT) model of two relativistic free massive neutrinos.
A simple expression to compute the quantum discord between two orbitals in fermion systems is derived using the parity superselection rule. As the correlation between orbitals depends on the basis chosen, we discuss a special orbital basis, the natural one. We show that quantum correlations between natural orbital pairs disappear when the pairing tensor is zero, i.e., the particle number symmetry is preserved. The Hartree-Fock orbitals within a Slater determinant state, Hartree-Fock-Bogoliubov quasiparticle orbitals in a quasiparticle vacuum, or the ground state of a Hamiltonian with particle symmetry and their corresponding natural orbitals are some relevant examples of natural bases and their corresponding states. Since natural orbitals have that special property, we seek the quantum discord in non-natural orbital bases. We analyze our findings in the context of the Lipkin-Meshkov-Glick and Agassi models.