Quantum Field Theoretic Treatment of Pion Production via Proton Synchrotron Radiation in Strong Magnetic Fields: Effects of Landau Levels

We study pion production from proton synchrotron radiation in the presence of strong magnetic fields. We derive the exact proton propagator from the Dirac equation in a strong magnetic field by explicitly including the anomalous magnetic moment. In this exact quantum-field approach the magnitude of pion synchrotron emission turns out to be much smaller than that obtained in the semi-classical approach. However, we also find that the anomalous magnetic moment of the proton greatly enhances the production rate about by two order magnitude.