Quantum Electrodynamics in Strong Magnetic Fields. IV. Electron Self-energy

Abstract

The electron self-energy in a magnetic field is calculated with the effect of the field included exactly. A new representation of the wavefunctions and other quantities is defined, in which the mass operator has a particularly simple form. After renormalisation, the form of the mass operator allows corrections to the Dirac equation, wavefunctions, vertex function and the electron propagator close to the mass shell to be calculated to lowest order in the fine structure constant. The probability for an electron to change spin while remaining in the same Landau level is calculated, and is found to be much less than the probability of cyclotron emission.