It can be easily checked that the self-energy contributions into the mass renormalization
are defined by electroweak and H-pion loops.
The mass renormalization is, however, a subtle problem, and unfortunately, we cannot yet find constants [gamma] and [b.sub.0] such as in (10).
Hiroshima and Spohn  study a perturbative mass renormalization including fourth order in the coupling constant in the case of a spinless electron.
Spohn, "Mass renormalization in nonrelativistic quantum electrodynamics," Journal of Mathematical Physics, vol.
In this section, we examine the physical explanation of QED phenomena provided by this theory, including self-energy and mass renormalization.
8.2 Dislocation strain energy and QED mass renormalization
This approach also resolves and eliminates the mass renormalization problem.
In the next section, we give the calculations of thermal corrections to the mass renormalization constant [delta]m/m of QED and the physical mass of electrons at finite temperatures.
In this range of temperature, the largest thermal contributions come from the mass renormalization constant.
(iii) Perhaps, most surprisingly, the scalar mass appearing in (30) is already the physically renormalized one, implying that the worldline instanton approach automatically takes all mass renormalization counterdiagrams into account.
At two loops, the numerical calculations of  confirm this, but only if physical mass renormalization is used!
Thus in 2D the leading asymptotic growth of the coefficients increases with increasing loop order, as it does in the 4D case before mass renormalization, and correspondingly it can be shown that the contributions to the EHL from mass renormalization are asymptotically subleading and thus irrelevant for our purposes (although the fermion propagator in 2D does not have UV divergences, mass renormalization is still a quite nontrivial issue; see  and refs.