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In a previous paper, we derived the quantum states of a Dirac particle in acircular, intense magnetic field in the limit of low momentum perpendicular tothe field with the purpose of giving a quantum description of the trajectory ofan electron, or a positron, in a typical pulsar or magnetar magnetosphere. Herewe continue this work by computing the radiation resulting from transitionsbetween these states. This leads to derive from first principles a quantumtheory of the so-called curvature and synchro-curvature radiations relevant forrotating neutron-star magnetospheres. We find that, within the approximation ofan infinitely confined wave-function around the magnetic field and in thecontinuous energy-level limit, classical curvature radiation can be recoveredin a fully consistent way. Further we introduce discrete transitions to accountfor the change of momentum perpendicular to the field and derive expressionsfor what we call quantum synchro-curvature radiation. Additionally, we expressdeconfinement and quantum recoil corrections.

Quantum theory of curvature and synchro-curvature radiation in a strong and curved magnetic field, and applications to neutron star magnetospheres