Spin operator and entanglement in quantum field theory

Abstract

Entanglement is studied in the framework of Dyson's S-matrix theory in relativistic quantum field theory, which leads to a natural definition of entangled states of a particle-antiparticle pair and the spin operator from a Noether current. As an explicit example, the decay of a massive pseudo-scalar particle into a pair of electron and positron is analyzed. Two spin operators are extracted from the Noether current. The Wigner spin operator characterizes spin states at the rest frame of each fermion and, although not measurable in the laboratory, gives rise to a straightforward generalization of low-energy analysis of entanglement to the ultrarelativistic domain. In contrast, if one adopts a (modified) Dirac spin operator, the entanglement measured by spin correlation becomes maximal near the threshold of the decay, while the entanglement is replaced by the classical correlation for the ultrarelativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables type of description is possible. Chiral symmetry differentiates the spin angular momentum and the magnetic moment. The use of weak interaction that can measure helicity is suggested in the analysis of entanglement at high energies instead of a Stern-Gerlach apparatus, which is useless for the electron. A difference between the electron spin at high energies and the photon linear polarization is also noted. The Standard Model can describe all of the observable properties of leptons.

Entanglement of Dirac bi-spinor states driven by Poincaré classes of SU(2)⊗SU(2) coupling potentials

“…To summarize, given that the Dirac equation is the equation of motion for fermionic fields [23], the entanglement content of Dirac particles [36][37][38] may also have a formulation extended to the context of Dirac fields, as in the description of fermion mixing [39] and neutrino oscillations [40]. …”

Majorana neutrino as Bogoliubov quasiparticle

“…This subject, besides an interest in the quantum information carried by ultra-relativistic particles [21], may become relevant in the future if one takes the Majorana fermion as a fundamental entity of Nature.…”

Entanglement entropy between real and virtual particles inϕ4quantum field theory

“…In this case, the quantum entropy computed is not important. But it is useful in the case in which the virtual process converts to a real process, for example see [47], where the effect on the entanglement entropy of real particles coming from a common virtual pair is considered or the opposite process where a massive pseudoscalar particle decays into a particle-antiparticle pair (see [48]). For example, if the first order contribution to the vacuum correlation function is considered and one of the loop propagators is cut, then we obtain the partial trace over the internal degrees of freedom of the first order contribution of the two-point correlation function.…”