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Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions

M. P. Fry
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Abstract

It is known that the one-loop effective action of ${QED}_2$ is a quadratic in the field strength when the fermion mass is zero: all potential higher order contributions beyond second order vanish. For nonzero fermion mass it is shown that this behavior persists for a general class of fields for at least one value of the fermion mass when the external field's flux $Φ$ satisfies $0<|eΦ|<2π$. For ${QED}_4$ the mass-shell renormalized one-loop effective action vanishes for at least one value of the fermion mass for a class of smooth, square integrable background gauge fields provided a plausible zero-mass limit exists.

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M. P. Fry. 2005-12-12. Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions. https://doi.org/10.1103/physrevd.62.125007%2010.1103%2Fphysrevd.72.109903

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