A precise pseudodifferential Foldy-Wouthuysen transform for the Dirac equation
type: Item
instance of: scholarly article
title: A precise pseudodifferential Foldy-Wouthuysen transform for the Dirac equation
zbMATH Open document ID: 1056.35110
published in: Journal of Evolution Equations
publication date: 2004-10-28T00:00:00Z
review text: The author discusses the existence of a unitary pseudodifferential operator \(U\) in the algebra of strictly classical pseudodifferential operators on \({\mathbb R}^3\) such that \(U\) precisely decouples the electronic and positronic part of the Dirac equation \(\partial\psi/\partial t+H\psi=0\) with the Dirac Hamiltonian \(H\) acting on \(x=(x_1,x_2,x_3)\). This situation holds for rather general potentials and without supersymmetry. A spectral split is introduced which can amount to a clean split into an electron and positron part of the Hamiltonian. Accordingly, a new algebra \(Q\) of precisely predictable observables amounts to a restriction of observables to those which are also reduced by this split. This interpretation makes the 1-particle Dirac theory consistent and thus eliminates a compelling need for Fermi-Dirac statistics since one no longer has to worry about negative energy states.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 81Q99
zbMATH DE Number: 2111545
zbMATH Keywords: decoupling
zbMATH Keywords: 1-particle Dirac theory
author: Heinz Cordes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2111545