Correction terms Coulomb screened, self energy

In this paper, we investigate the correction terms obtained when applying a covariant Pauli-Villars regulator [16] when formulating the PWR procedure. In Section II we consider the first-order self energy and the Coulomb screened self energy is discussed in Section III. Finally, we derive an expression suitable for numerical evaluation of the correction term in the Coulomb screened case. 

We will show below that this correction term vanishes for the first-order self energy and cancels for the Coulomb-screened self energy. This is, however, not always the case for higher-order effects. As an example, for the self energy in an external magnetic potential the correction term gives rise to a finite shift... 

In the partial-wave renormalization approach, which we consider in this paper, we have shown that these correction terms vanish for the first-order selfenergy and also for Coulomb screened self-energy. However, in the last case we obtain non-zero correction terms for the different subgroups of diagrams,... 

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