Relativistic quantum electrodynamics without antiparticles, electron-laser interaction and primary cosmic rays: near the classical limit

The dynamics of relativistic (up to 10 GeV) electrons in high-intensity electron-laser interactions (up to near ultraviolet), close to the classical limit, previously suggested that a relativistic Quantum Electrodynamics (QED) framework excluding positrons could provide deeper insights. This hypothesis was based on scarce experimental positron detections and numerical computations. Motivated by this, the present work analyzes relativistic quantum electrodynamical descriptions near the classical limit. We perturbatively study this modified QED model, focusing on Compton scattering (yielding a Klein–Nishina-like formula that excludes virtual positrons), ultraviolet divergences, and the electron anomalous magnetic moment. The model yields the following key results: i) Lacking explicit Lorentz covariance, it deviates more markedly from full relativistic QED (which includes positrons) as both the energy and the contribution of electron–positron loops increase; notably, the electron anomalous magnetic moment differs by about 60% between the two theories. ii) It reproduces the Thomson limit, suggesting increasing reliability closer to the classical limit. iii) It suggests a relativistic Quantum Mechanics framework without negative energies in external fields, involving square root operators. The spinless case is studied, and the spin-1/2 case (complementing the standard Dirac equation) is shown to be consistent with the non-relativistic quantum (Pauli) equation. Both relativistic wave equations consistently yield the classical relativistic limit (restoring Lorentz covariance) without negative energies. Finally, this approach is extended to primary cosmic rays in outer space, which consist mostly of protons (with very scarce antiprotons), some electrons (with fewer positrons), and smaller fluxes of α particles, 8 16 O , 6 12 C , and 26 56 Fe nuclei, while their corresponding antiparticles remain undetected. We conclude that scalar relativistic QED excluding antiparticles (with radiation up to x-rays), along with the related relativistic wave equations, may provide a better understanding of spinless primary cosmic rays near the classical limit.