English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In this paper we study in detail the connection between the solutions to theDirac and Weyl equation and the associated electromagnetic 4-potentials. First,it is proven that all solutions to the Weyl equations are degenerate, in thesense that they correspond to an infinite number of electromagnetic4-potentials. As far as the solutions to the Dirac equation are concerned, itis shown that they can be classified into two classes. The elements of thefirst class correspond to one and only one 4-potential, and are callednon-degenerate Dirac solutions. On the other hand, the elements of the secondclass correspond to an infinite number of 4-potentials, and are calleddegenerate Dirac solutions. Further, it is proven that at least two of these4-potentials are gauge-inequivalent, corresponding to different electromagneticfields. In order to illustrate this particularly important result we havestudied the denerate solutions to the force-free Dirac equation and shown thatthey correspond to massless particles. We have also provided explicit examplesregarding solutions to the force-free Weyl equation and the Weyl equation for aconstant magnetic field. In all cases we have calculated the infinite number ofdifferent electromagnetic fields corresponding to these solutions.

On the connection between the solutions to the Dirac and Weyl equations and the corresponding electromagnetic 4-potentials