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 ultra-relativistic 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 ultra-relativistic electron-positron pair by analogy to the case of neutrinos, for which a hidden-variables-type 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 the observable properties of leptons.

17 pages. Substantially modified and extended. The title has been changed. To appear in PRD

References in corpus (8)

• Hidden Variables and the Two Theorems of John Bell
• Einstein-Podolsky-Rosen correlations of Dirac particles - quantum field theory approach
• Physical interpretation of the Wigner rotations and its implications for relativistic quantum information
• What is the relativistic spin operator?
• Relativistic spin operators in various electromagnetic environments
• Spin quantum correlations of relativistic particles
• Does CHSH inequality test the model of local hidden variables?
• Linearity of quantum probability measure and Hardy's model

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• Entanglement entropy between real and virtual particles in ${\varphi }^4$ quantum field theory
• Lorentz Invariant Quantum Concurrence for SU(2) x SU(2) spin-parity states