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

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 $\Phi$ satisfies $0<|e\Phi |<2\pi$. 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.

Section IV has been amended

References in corpus (3)

• On the QED Effective Action in Time Dependent Electric Backgrounds
• Borel Summation of the Derivative Expansion and Effective Actions
• Chiral limit of the two-dimensional fermionic determinant in a general magnetic field

Cited by in corpus (5)

• Quantum diffusion of magnetic fields in a numerical worldline approach
• Fermion determinant for general background gauge fields
• Evidence for mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics
• Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field
• The symmetries of the Dirac--Pauli equation in two and three dimensions