CPT symmetry for relativistic particles in the presence of a topologically chiral magnetic field

The prediction of antimatter is one of the most notable triumphs of relativistic quantum mechanics present in the solutions to the Dirac equation (DE). However, this equation presents a difficulty in analytically calculating energy spectra and the corresponding wave functions. Consequently, the study of the DE has been limited to a small set of scalar potentials, or the behavior of this equation in the presence of vector potentials has only been described.

In this research, ED is used to model the behavior of a relativistic electron interacting with a topologically chiral magnetic field whose envelope traces a helicoid perpendicular to the particle's direction of propagation. The ED is solved analytically using the Markowitz-Schwinger formalism, getting the spectrum of eigenvalues, which, once known, are used in a direct calculation to recover the eight corresponding spinors. This type of system presents a novel region of forbidden energies in addition to the mass gap, characteristic of the relativistic nature of particles. The new region corresponds to a segregating region depending on the spin of the particle.

Since the eigenvalue spectrum is defined analytically, in this research, we constructed energy operators and spin projectors that reflect the segregating structure of the system. On the other hand, having recovered the eigen-spinors analytically allowed us to evaluate the charge conjugation, time reversal, and parity symmetries, verifying the validity of the CPT theorem. Although the validity of this theorem with respect to the mass gap is known in the literature, this research showed for the first time that these symmetries are also preserved in energy segregating regions.