First quantized pair interactions, fermion loops and entanglement

TL;DR

This paper explores the formulation of quantum electrodynamics through pair interactions, fermion loops, and entanglement, extending relativistic quantum mechanics to include pair creation and annihilation, and analyzing entanglement restrictions.

Contribution

It introduces an extended parametrized formalism for pair interactions and entanglement, justified with plane wave summations, and develops an invariant Bell's inequality for spin-1/2 particles.

Findings

Entanglement is restricted to the Compton wavelength in QFT.

The extended formalism accounts for pair creation and annihilation.

An invariant Bell's inequality for spin-1/2 is derived.

Abstract

Quantum Electrodynamics may be formulated as a Quantum Field Theory , and also as relativistic quantum mechanics by introduction of the Feynman-Stueckelberg parameter. As stated by M. Srednicki ({\it Quantum Field Theory}, Cambridge University Press, Cambridge and New York, 2007), "\dots any relativistic quantum physics that can be treated in one formalism can also be treated in the other". Entanglement of electrons at macroscopic spacelike separation has been observed (B. Hensen {\it et al.}, Nature, $\bf{526}$, 2015, doi:10.1038.nature/15759), yet according to Quantum Field Theory is restricted to separations of the order of the Compton wavelength $\hbar/m_e c$ (see e.g., S. J. Summers and R. Werner, Commun. Math. Phys. $\bf{110}$,247,1987). There is no restriction on entanglement in parametrized relativistic quantum mechanics (A. F. Bennett, Ann. Phys. $\bf{345}$, 1, 2014). The parametrized formalism is extended here to pair annihilation and pair creation. The {\it ansatz} used in the formalism to develop the correct higher order corrections is justified here with plane wave summations. The conflict over entanglement is further discussed in terms of the Klein-Gordon propagator, and an invariant Bell's inequality is developed for spin -1/2.