Abstract
In our Comment we question the validity of the claim made by Campos and Cabrera [Phys. Rev. Res. 2, 013051 (2020)] that their solutions of the Dirac equation in an external time-dependent electromagnetic field describe beams of electrons. In every time-dependent field, no matter how weak, which has an infinite time duration, there is continuous electron-positron pair creation and annihilation. Without the proper accounting for these processes, the mathematical solutions of the Dirac equation are not directly applicable to realistic physical situations. In particular, the time evolution of the average values $\ensuremath{\langle}x\ensuremath{\rangle}$ and $\ensuremath{\langle}y\ensuremath{\rangle}$ does not describe the electron trajectory but the motion of some combination of the electron and positron charge distributions with pathological properties (zitterbewegung).
Highlights
In their work [1] the authors present new analytical solutions of the Dirac equation hoping that “the analytical solutions of the Dirac equation given here provide important insights into the relativistic dynamics of electrons.” We do not question the validity of their formulas and we praise the authors for inventing a new method to generate solutions of the Dirac equation in an electromagnetic field
In order to use a solution of the Dirac equation to describe the motion of the electron wave packets, one must be sure that the part describing the motion of electrons has been separated from the full solution
We will show in what follows that even the simplest Wolkow solution of the Dirac equation [3] has a part that describes positrons
Summary
In their work [1] the authors present new analytical solutions of the Dirac equation hoping that “the analytical solutions of the Dirac equation given here provide important insights into the relativistic dynamics of electrons.” We do not question the validity of their formulas and we praise the authors for inventing a new method to generate solutions of the Dirac equation in an electromagnetic field. The Dirac equation in the presence of any time-dependent electromagnetic field is not an equation describing just the evolution of a wave packet of an electron. In order to use a solution of the Dirac equation to describe the motion of the electron wave packets, one must be sure that the part describing the motion of electrons has been separated from the full solution.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
