Abstract
The one-loop effective action describing polarization of the vacuum due to virtual electron-positron pairs in the Maxwell theory of electromagnetism was obtained by Heisenberg and Euler, in the limit of a background field that is constant on the scale of the electron Compton-wavelength. The case of vanishing electric field and constant, ultra-strong magnetic field B≫Bc, where [Formula: see text], yields a configuration whose energy density is less than that of the equivalent radiation field, suggesting why a magnetic field may be present in the early Universe back to the Planck era. For there is a similar but larger effect, allowing a "ferromagnetic" Yang–Mills vacuum state, in the grand-unified theory at temperatures [Formula: see text], analyzed by Skalozub. Some further aspects of ultra-strong magnetic fields are discussed vis-à-vis the origin of the Galactic field B g .
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