Degenerate solutions to the Dirac and Weyl equations and their applications

Abstract

In this review article we present a comprehensive review of degenerate solutions to the Dirac and Weyl equations, highlighting novel and significant findings. Specifically, we demonstrate that all Weyl particles, and under certain conditions Dirac particles, can occupy the same quantum state under an extensive range of electromagnetic 4-potentials and fields. These fields, which are infinite in number, have been explicitly derived and analysed. Additionally, we establish that Weyl particles can form localized states even in the absence of external electromagnetic fields. Moreover, we show that their localization can be precisely controlled through the application of simple electric fields, offering a tuneable mechanism for manipulating these particles. Building on these insights, we propose an innovative device that utilizes Weyl fermions to control the flow of information at an unprecedented rate of up to 100 petabits per second. This finding has significant implications regarding the development of next-generation electronic and quantum information technologies, as it presents a fundamentally new approach to high-speed data processing and transmission.