High Energy Particle Production from Proton Synchrotron Radiation in Strong Magnetic Fields in Relativistic Quantum Field Theory

We investigate photon, pion, and rho-meson production from proton synchrotron radiation in the presence of strong magnetic fields. The proton decay widths and the luminosities of the emitted particles are calculated within a relativistic quantum framework that incorporates Landau quantization. A scaling rule is derived for the transition probability between different Landau levels. This allows an evaluation of transitions for extremely high Landau numbers exceeding ${10}^{15}$. Furthermore, we calculate the momentum distribution of the emitted particles by properly including the proton recoil effect associated with particle emission. The results differ significantly from conventional semiclassical approaches.