A General Method for Obtaining Degenerate Solutions to the Dirac and Weyl Equations and a Discussion on the Experimental Detection of Degenerate States

• Published in: Annalen der Physik 2023-04, Vol.535 (4), p.n/a
• Main Authors: Tsigaridas, Georgios N., Kechriniotis, Aristides I., Tsonos, Christos A., Delibasis, Konstantinos K.
• Format: Article
• Language: English
• Subjects: degenerate solutions; Dirac equation; Dirac particles; electromagnetic 4‐potentials; electromagnetic fields; Mathematical analysis; Weyl particles
• ISSN: 0003-3804; 1521-3889
• DOI: 10.1002/andp.202200647

In this work, a general method is described for obtaining degenerate solutions of the Dirac equation, corresponding to an infinite number of electromagnetic 4‐potentials and fields, which are explicitly calculated. More specifically, using four arbitrary real functions, one can automatically construct a spinor that satisfies the Dirac equation for an infinite number of electromagnetic 4‐potentials, defined by those functions. An interesting characteristic of these solutions is that, in the case of Dirac particles with nonzero mass, the degenerate spinors should be localized, both in space and time. The method is also extended to the cases of massless Dirac and Weyl particles, where the localization of the spinors is no longer required. Finally, two experimental methods are proposed for detecting the presence of degenerate states. A general method for obtaining degenerate solutions to the Dirac equation is presented. In more detail, using four arbitrary real functions, one can automatically construct a spinor that satisfies the Dirac equation for an infinite number of electromagnetic 4‐potentials, defined by these functions. The method is also extended to the cases of massless Dirac and Weyl equations.