Feynman-Stueckelberg electroweak interactions and isospin entanglement

Abstract

Entanglement in Quantum Field Theory is restricted to spacelike separations to the order of the Compton wavelength $\hbar/mc$ (e.g., S. J. Summers and R. Werner, {\it J. Math. Phys.}, {\bf 28}, 10,2440-2447, (1987)). Yet spin entanglement of electrons across macroscopic distances has been observed by Hensen { \it et al.} ({\it Nature}, {\bf 526}, doi:10.1038/nature/15759, (2015)). The parametrized relativistic quantum mechanics of Feynman and Stueckelberg admits spin singlets, across arbitrary separations, by providing a single covariant wave equation for tensor products of two Dirac spinors (A. F. Bennett, {\it Ann. Phys.} {\bf 345}, 1-16 (2014)). The formalism is extended here from quantum electrodynamics to the electroweak interaction. A relativistic Bell's inequality for Dirac spinors is extended here to weak isospin.