Here, the first term j ϵ ∞ j in the third line of Eqn. 36 is a time-independent infinite quantity that is referred to as the self-energy (not to be confused with the dipole self-energy), which can be regarded as a shift of the zero-point energy and is dropped in the last line of the above equation. In short, the Coulomb potential V coul (x) ≡ V (x) emerges from the longitudinal electric field.