Quantum field theory analysis of polarizations correlations, entanglement and Bell's inequality: explicit processes

Abstract

Key words Quantum field theory specific calculations, polarization correlations, entanglement and Bell's inequality, applications to QED, electroweak theory and strings This paper provides explicit and detailed quantum field theory (QFT) computations of polarizations correlations of emerging particles in several processes in QED, Electroweak Theory, and even in particle productions from strings, and hence are based on dynamical theries. The novel properties observed in the computations of such polarizations correlations, as predicted by QFT, is that they depend on the speed of the colliding particles, and, in some cases, even on coupling parameters ratios as well as on mass ratios of the underlying theory. These investigations clearly show that arguments based simply on combining spins to generate probabilities of such polarization correlations are not reliable. The novel properties obtained, with details of derivations provided here, hopefully would call for experiments on polarizations correlations which would monitor speeds of colliding particles, and, would, in turn, lead to new tests of the fundamental interactions of QFT such as of QED and of the Electroweak Theory.

The effect of time-dilation on Bell experiments in the retrocausal Brans model

“…These challenges have been addressed, mainly in the context of relativistic quantum information theory, to varying degrees. Several authors [67][68][69][70][71] have described the EPR and Bell correlations in relativistic settings using quantum field theory, but the timeevolution of the spin measurements, which is the issue at stake here, has not been addressed. The authors of [66] propose a general formalism to describe localized massive fermions in curved space-time, which they use in [72] to give a detailed description of relativistic Stern-Gerlach measurements on a single fermion.…”

“…These challenges have been addressed, mainly in the context of relativistic quantum information theory, to varying degrees. Several authors [28][29][30][31][32] have described the EPR and Bell correlations in relativistic settings using quantum field theory, but the time-evolution of the spin measurements, which is the issue at stake here, has not been addressed. The authors of ref.…”

Entanglement and scattering in quantum electrodynamics: S-matrix information from an entangled spectator particle

“…Such diagonal elements, which play a key role in the determination of S C z , have terms proportional to diagonal elements of the initial density matrix of the system A, namely cos 2 α and sin 2 α besides a term proportional to E 7 . These diagonal elements are interchanged in the states |Ψ ± and |Φ ± as can be seen from the density matrices given by the equations ( 38) and (39), respectively. This feature can be observed in the graphs depicted in figure 7a and 7b, where the variation of the spin measured for system C in the z-direction is plotted as a function of the energy E and the angle α that char-acterises the initial spin state of system A.…”

“…Because such a quantity is proportional to the cross-section, it was explicitly verified through appropriate Wigner rotations that it is Lorentz invariant whilst the correlations involving only spin degrees of freedoms is not. Bell's inequality violation in QED was verified in the process 2γ → e + e − [39] shedding light on its experimental measurement.…”

Momentum correlations of scattered particles in quantum field theory: one-loop entanglement generation

“…There exist a plethora of applications of scattering and entanglement generation. For example in [18] it is studied the violation of Bell's inequalities in polarization correlations in the Standard Model [18] and in [19] they analyse the "EPR=ER" conjecture of Maldacena and Susskind in a four gluon scattering represented by open strings. The generation and degree of entanglement in fermionic scattering within quantum electrodynamics was analysed in [20] and a study of entropy variation between initial and final states asymptotic states to leading order in perturbation theory appears in [21].…”