Abstract
We revisit the calculation of the fermion self-energy in QED in the presence of a magnetic field. We show that, after carrying out the renormalization procedure and identifying the most general perturbative tensor structure for the modified fermion {mass operator} in the large field limit, the mass develops an imaginary part. This happens when account is made of the sub-leading contributions associated to Landau levels other than the lowest one. The imaginary part is associated to a spectral density describing the spread of the mass function in momentum. The center of the distribution corresponds to the magnetic-field modified mass. The width becomes small as the field intensity increases in such a way that for asymptotically large values of the field, when the separation between Landau levels becomes also large, the mass function describes a stable particle occupying only the lowest Landau level. For large but finite values of the magnetic field, the spectral density represents a finite probability for the fermion to occupy Landau levels other than the LLL.
Highlights
Magnetic fields influence the propagation properties of electrically charged as well as of neutral particles
In order to find the magnetic fielddriven mass corrections, several calculations [8,9,10,11,12] resort to finding the self-energy matrix element in the fermion preferred state, namely, the spinor representing the lowest energy fermion state
We carry out the computation of the magnetic field induced fermion self-energy and from its general structure, we find the mass and width
Summary
Magnetic fields influence the propagation properties of electrically charged as well as of neutral particles. In order to find the magnetic fielddriven mass corrections, several calculations [8,9,10,11,12] resort to finding the self-energy matrix element in the fermion preferred state, namely, the spinor representing the lowest energy fermion state For these purposes, Schwinger’s phase factor is kept all along the calculation, which makes it a bit more cumbersome since the kinematical momentum Πμ 1⁄4 pμ − eAμðxÞ, instead of the canonical momentum pμ, is involved, where AμðxÞ is the four-vector potential that gives rise to the magnetic field. VI and leave for the appendices the explicit computation of some of the expressions and calculations that we use throughout the rest of the work
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