The Stueckelberg wave equation and the anomalous magnetic moment of the electron

Abstract

The parametrized relativistic quantum mechanics of Stueckelberg [Helv. Phys. Acta 15, 23 (1942)] represents time as an operator, and has been shown elsewhere to yield the recently observed phenomena of quantum interference in time, quantum diffraction in time and quantum entanglement in time. The Stueckelberg wave equation as extended to a spin-1/2 particle by Horwitz and Arshansky [J. Phys. A: Math. Gen. 15, L659 (1982)] is shown here to yield the electron g-factor g = 2 (1 + α/2π), to leading order in the renormalized fine structure constant α, in agreement with the quantum electrodynamics of Schwinger [Phys. Rev., 73, 416L (1948)].

Induced representations of tensors and spinors of any rank in the Stueckelberg-Horwitz-Piron theory

“…The 1-loop correction to the magnetic moment of a particle evolving with the Hamiltonian (3.14) was calculated by Bennett [24] , resulting in a value compatible with the one obtained by renormalization of the vertex function in QFT [25] .…”

“…It has the same form as a second order Dirac equation, but the coupling to the spin is purely magnetic through the induced representation. It contains the correct gyromagnetic ratio and, as shown by Bennett [24] , accounts as well, to lowest order, for the anomalous moment, and provides the same energy spectrum in the nonrelativistic limit [8] .…”

Relativistic entanglement

“…when n µ → (1, 0, 0, 0). i.e., P n± corresponds to a helicity projection.Therefore the matrix elements of the S-matrix at any point on the orbit of the induced representation is equivalent (by replacing S by U (L(n))SU −1 (L(n))) to the corresponging helicity representation associated with the frame in which n µ is n 0 The anomalous magnetic moment of the electron can be computed in this framework (Bennett [19]) without appealing to the full quantum field theory of electrodynamics.…”

“…The anomalous magnetic moment of the electron can be computed in this framework (Bennett [19]) without appealing to the full quantum field theory of electrodynamics.…”

Spin, angular momentum and spin-statistics for a relativistic quantum many-body system

“…The expression ( 13) is quite similar to that of the second order Dirac operator; it is, however, Hermitian and has no direct electric coupling to the electromagnetic field in the special frame for which n µ = (1, 0, 0, 0) in the minimal coupling model we have given here (note that in his calculation of the anomalous magnetic moment [18], Schwinger puts the electric field to zero; a non-zero electric field would lead to a non-Hermitian term in the standard Dirac propagator, the inverse of the Klein-Gordon square of the interacting Dirac equation). Note that in the derivation of the anomalous magnetic moment given by Bennett [19], this restriction is not necessary since the generator of the interacting motion is intrinsically Hermitian.…”