Contribution of vacuum fluctuation to the self-energy of the electron

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Main Question or Discussion Point

In the book" The Quantum Theory of Radiation", Heitler derived the transverse self-energy of the electron(Chapter III, Section18, Eq.(23))

$$\frac{{{e^2}}}{{\pi m}}\int_{\text{0}}^\infty {kdk} $$
which is the energy of the electron under the action of the vacuum fluctuation of the
radiation field. But it is one half of Weisskopf's result( (Phys. Rev. 56, 72,1939: page 81). Why? I can't figure it out.
 

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