Anomalous particles

Besides the fermions of Dirac, Weyl, and Majorana there is the different type of fermions referred to as anomalous. The Dirac wave equation, in addition to conventional solutions, has different ones corresponding to anomalous particles, which are independent. The concept of anomalous particles is applicable to Dirac insulators, where electrons obey the Dirac-like wave equation. Positively charged antielectrons, which are not holes, can exist in the Dirac insulator. In this material one can create the electron-antielectron pair keeping the valence band completely filled. The anomalous quantum state, associated with the electron-antielectron vacuum, is an inner property of the Dirac insulator.

💡 Research Summary

The manuscript proposes a new class of fermionic excitations, termed “anomalous particles,” which are claimed to arise as independent solutions of the Dirac equation, distinct from the conventional Dirac, Weyl, and Majorana states. The author begins by recalling the standard Dirac formalism: the Dirac equation admits positive‑energy (ψ⁺) and negative‑energy (ψ⁻) plane‑wave solutions that can be expanded in a complete set of spherical spinor harmonics ψ_{q,j,l,m}. These conventional eigenfunctions form a basis for any free‑particle wavefunction.

A key step is the introduction of a spin‑space transformation ψ = exp(λσ_z) ψ′ with λ = (1/4)ln