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Evidence for mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics

M. P. Fry
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Abstract

The Euclidean fermionic determinant in four-dimensional quantum electrodynamics is considered as a function of the fermionic mass for a class of $O(2)\times O(3)$ symmetric background gauge fields. These fields result in a determinant free of all cutoffs. Consider the one-loop effective action, the logarithm of the determinant, and subtract off the renormalization dependent second-order term. Suppose the small-mass behavior of this remainder is fully determined by the chiral anomaly. Then either the remainder vanishes at least once as the fermionic mass is varied in the interval $0 < m < \infty$ or it reduces to its fourth-order value in which case the new remainder, obtained after subtracting the fourth-order term, vanishes at least once. Which possibility is chosen depends on the sign of simple integrals involving the field strength tensor and its dual.

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M. P. Fry. 2010-04-19. Evidence for mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics. https://doi.org/10.1103/physrevd.75.065002%2010.1103%2Fphysrevd.75.069902

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