Fermion self-energy

The fermion self-energy is the amputated one-particle-irreducible two-point function

Σ (\neq p)

. It corrects both the coefficient of

\neq p

and the fermion mass and thereby shifts the pole and residue of the exact propagator.

Table of contents
- Electron self-energy Fermion self-energy
- QED one-loop running-mass to pole-mass conversion Fermion self-energy

Electron self-energy ( $Σ (p)$ )

The fermion self-energy of an electron in quantum electrodynamics. After renormalization, its contribution in a bound chemical atom is one source of the Lamb shift; other radiative corrections and nuclear structure also affect the observed energy levels.

QED one-loop running-mass to pole-mass conversion ( $m_{\overline{MS}} (μ) = m_{pole} [1 - \frac{e ^{2}}{16 π ^{2}} (5 + 3 lo g (μ^{2} / m_{pole}^{2}))] + O (e^{4})$ )

In quantum electrodynamics, the modified minimal subtraction scheme running mass differs from the perturbative pole mass by a finite correction. The displayed relation follows by evaluating the renormalized fermion self-energy at the mass shell and imposing a zero of the inverse Dirac propagator. The sign assigned to the self-energy insertion must be matched to its denominator convention; changing that naming convention does not change the conversion. A wave-function coefficient counterterm and multiplicative mass renormalization are also distinct: the coefficient of the mass term includes both at first order.

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