Reply to “Comment on ‘Nondispersive analytical solutions to the Dirac equation’ ”

Abstract

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-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)10.1103/PhysRevResearch.2.013051].