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

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.

48 pages, 2 figures, Typos and changes to Eqs. (121),(125),(126),(127),(134) and (A5).

References in corpus (2)

• Precise Quark Mass Dependence of Instanton Determinant
• Calculation of QCD Instanton Determinant with Arbitrary Mass

Cited by in corpus (8)

• Nonperturbative results for the mass dependence of the QED fermion determinant
• Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field
• Non-perturbative quantization of the electroweak model's electrodynamic sector
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• Non-perturbative path integral quantization of the electroweak model: the Maxwell integration
• Strong, Random field behavior of the Euclidean Dirac propagator
• QED effective action for an O(2)xO(3) symmetric field in the full mass range
• New asymptotic techniques for the partial wave cut-off method for calculating the QED one loop effective action