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A precise pseudodifferential Foldy-Wouthuysen transform for the Dirac equation

A precise pseudodifferential Foldy-Wouthuysen transform for the Dirac equation We will discuss existence of a unitary pseudodifferential operator U in our algebra $$ Op\psi c_0 $$ of strictly classical pseudodifferential operators on $$ \bf{R^3} $$ such that U precisely decouples the “electronic” and ”positronic” part of the Dirac equation, for rather general potentials, and without supersymmetry. Interestingly, an obstruction appears: On may have to remove a finite dimensional space of “electronic” states, and declare them as “positronic”, or, vice versa, depending on a certain deficiency index. Possibly, this index is nonzero if electronic bound states penetrate into the positronic continuous spectrum, or vice versa. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

A precise pseudodifferential Foldy-Wouthuysen transform for the Dirac equation

Cordes, H.
Journal of Evolution Equations , Volume 4 (1) – Mar 1, 2004
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References (11)

Publisher
Springer Journals
Copyright
Copyright © 2004 by Birkhäuser-Verlag
Subject
Mathematics
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-003-0128-5
Publisher site
See Article on Publisher Site

Abstract

We will discuss existence of a unitary pseudodifferential operator U in our algebra $$ Op\psi c_0 $$ of strictly classical pseudodifferential operators on $$ \bf{R^3} $$ such that U precisely decouples the “electronic” and ”positronic” part of the Dirac equation, for rather general potentials, and without supersymmetry. Interestingly, an obstruction appears: On may have to remove a finite dimensional space of “electronic” states, and declare them as “positronic”, or, vice versa, depending on a certain deficiency index. Possibly, this index is nonzero if electronic bound states penetrate into the positronic continuous spectrum, or vice versa.

Journal

Journal of Evolution Equations – Springer Journals

Published: Mar 1, 2004

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