Abstract
The one-loop effective action of quantum electrodynamics in four dimensions is shown to be controlled by the Euclidean Dirac propagator $G$ in a background potential. After separating the photon self-energy and photon-photon scattering graphs from the effective action the remainder is known to be the logarithm of an entire function of the electric charge of order 4 under mild regularity assumptions on the potential. This input together with QED's lack of an ultrastable vacuum constrain the strong field behavior of $G$. It is shown that $G$ vanishes in the strong field limit. The relevance of this result to the decoupling of QED from the remainder of the electroweak model for large amplitude variations of the Maxwell field is discussed.
Highlights
It may seem surprising that anything more remains to be said about the quantized Euclidean Dirac field propagator G in four dimensions in a background potential Aμ, where
Intuition is helped by viewing Fμν in Euclidean space as a time-independent four-dimensional magnetic field
Competition between the diamagnetic ðp − eAÞ2 and paramagnetic eσF=2 terms in the exponentiated Hamiltonian in (1) remains an obstruction to the strong field analysis of G. It is the aim of this paper to demonstrate that G vanishes in the strong field limit for a broad class of potentials. It will be explained below why this is of physical interest
Summary
It may seem surprising that anything more remains to be said about the quantized Euclidean Dirac field propagator G in four dimensions in a background potential Aμ, where. The term strong field in this paper refers to the large amplitude variation of a random potential that occurs in a Euclidean functional integral over Aμ. Integrating out the fermion degrees of freedom results in an effective action depending on 6 lepton and 3 × 6 quark determinants from the neutral weak-current and 3 þ 3 × 3 determinants from the charged weak-current, including color, that are functionals of the Higgs, Maxwell, Z and W fields [5].
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