arXiv subjects

A. F. Bennett

Publications and source records attributed to A. F. Bennett.

5 recordsLinked to original sources

arXiv2023

Feynman-Stueckelberg electroweak interactions and isospin entanglement

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.

physics.gen-ph↗

arXiv2023

Duffin-Kemmer-Petiau particles are bosons

The parametrized Duffin-Kemmer-Petiau wave equation is formulated here for many relativistic particles of spin-0 or spin-1. The conventional second-quantized or Fock-space proof of the spin-statistics connection requires that the fields of creation and annihilation operators satisfy commutation relations subject to causality conditions. The conditions restrict entanglement to spacelike separations of the order of the Compton wavelength $\hbar/mc$. Relativistic quantum mechanics is used here to prove the symmetry of the wavefunctions for identical particles, following the nonrelativistic argument of Jabs (Found. Phys. 2010, v40, 776--792). First quantization does not require causal commutation relations, and so entanglement is unrestricted.

quant-ph↗

arXiv2020

First quantized pair interactions, fermion loops and entanglement

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.

quant-ph↗

arXiv2020

First Quantized Electrodynamics

The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe-Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED.

quant-ph↗

arXiv2020

Spin-Statistics Connection for Relativistic Quantum Mechanics

The spin-statistics connection has been proved for nonrelativistic quantum mechanics (Jabs, A., 2010: Found. Phys., {\bf 40}, 776-792). The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality condition is not required.

quant-ph↗