A new method was developed to solve the Dirac equation and used to find analytical solutions for time-dependent electromagnetic fields that translate a given Dirac spinor along any desired trajectory in the $x\text{−}y$ plane without distortion. As is well known, negative energy solutions describing antiparticles play a prominent role in the Dirac theory of the electron, and a separation of the part of the wave function describing only electrons from the full solutions often needs to be done. Here, we clarify how the aforementioned separation is done, which is not clear in our recent publication [Campos and Cabrera, Phys. Rev. Research 2, 013051 (2020)].

• Received 18 April 2020
• Accepted 12 June 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.038002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society