The 1-loop self-energy of an electron in a strong external magnetic field revisited

Bruno Machet (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

I revisit the 1-loop self-energy of an electron of mass m in a strong, constant and uniform external magnetic field B. First, I show, after Tsai (1974), how, for an electron in the lowest Landau level, Schwinger's techniques, as explained by Dittrich and Reuter (1985) lead to the same integral deduced by Demeur (1953) and used later by Jancovici (1969). Then, I calculate the Demeur-Jancovici integral in the range 75 =< L =< 10000, L=eB/m^2, which yields \delta m \simeq (\alpha*m/(4*\pi))*[(\ln L -\gamma_E -3/2)^2 -9/4 +\pi/(\beta-1) + \pi^2/6 +\pi*\Gamma[1-\beta]/L^{\beta-1} +(1/L)*(\pi/(2-\beta)-5) +{\cal O}(1/L^{>= 2})] with \beta \approx 1.175, very close numerically to Jancovici's last estimate \delta m \simeq (\alpha*m/(4*\pi))*[(\ln 2L -\gamma_E -3/2)^2 + A + ...] with A \approx 3.5 (undetermined by Jancovici). The (\ln L)^2, only contribution to be ever considered, gets largely damped, in particular by the large (\ln L) which arises from the counterterm implementing suitable renormalization conditions. The former exceeds by 45% the true estimate at L=100 and by more at lower L. The addition to existing literature is small but some consequences may be worth deeper investigations.

Mots clés: Quantum Electrodynamics; external magnetic field; electron self-energy

Domaines: Physique des Hautes Energies - Phénoménologie [hep-ph]

Bruno Machet. The 1-loop self-energy of an electron in a strong external magnetic field revisited. 2015. ⟨hal-01215168v2⟩