  Problems of self-interaction arise in both classical and quantum field
theories. To understand how such problems are to be addressed in a quantum
theory of the Dirac and electromagnetic fields (quantum electrodynamics), we
can start by analyzing a classical theory of these fields. In such a classical
field theory, the electron has a spread-out distribution of charge that avoids
some of the problems of self-interaction facing point charge models. However,
there remains the problem that the electron will experience self-repulsion.
This self-repulsion cannot be eliminated within classical field theory without
also losing Coulomb interactions between distinct particles. But, electron
self-repulsion can be eliminated from quantum electrodynamics in the Coulomb
gauge by fully normal-ordering the Coulomb term in the Hamiltonian. After
normal-ordering, the Coulomb term contains pieces describing attraction and
repulsion between distinct particles and also pieces describing particle
creation and annihilation, but no pieces describing self-repulsion.
