A note on the electron self‐energy Available to Purchase

Using dimensional regularization, the lowest‐order electron self‐energy function in an arbitrary covariant gauge is derived. For off‐mass‐shell electrons, the usual expression for the finite portion Σ_f of the self‐energy as the number of space‐time dimensions n approaches 4 is recovered. In the case of on‐mass‐shell electrons, the condition (p/−m)Σ_f→0 as p/→m, which is necessary to make the usual separation of the renormalization constant unambiguous, requires that n approach 4 from above, i.e., n→4₊. This necessary condition on Σ_f is not satisfied by the off‐mass‐shell expression in the limit p²→m² due to a branch point in the self‐energy operator.