Abstract
Strong background fields require a non-perturbative treatment, which is afforded in QED by the Furry expansion of scattering amplitudes. It has been conjectured that this expansion breaks down for sufficiently strong fields, based on the asymptotic growth of loop corrections with increasing "quantum nonlinearity", essentially the product of field strength and particle energy. However, calculations to date have assumed that the background is constant. We show here, using general plane waves of finite duration, that observables at high quantum nonlinearity scale differently depending on whether intensity or energy is large. We find that, at high energy, loop contributions to observables tend to fall with increasing quantum nonlinearity, rather than grow.
Highlights
A strong electromagnetic field is characterized by a dimensionless coupling to matter which is larger than one
Loop corrections appear to grow with higher powers of the effective coupling, and so when αχ2=3 ∼ 1 the Furry expansion breaks down
The calculations behind the conjecture have, been performed in constant crossed fields; these are the zero frequency limit of plane waves, commonly used as a first model of laser fields at ultrahigh intensity [11,12,13,14,15,16]. (We will typically refer to field intensity, rather than strength.) Notably, the power of 2=3 which appears is tied to the Airy functions particular to the constant field case
Summary
Strong background fields require a nonperturbative treatment, which is afforded in QED by the Furry expansion of scattering amplitudes. It has been conjectured that this expansion breaks down for sufficiently strong fields, based on the asymptotic growth of loop corrections with increasing “quantum nonlinearity,” essentially the product of field strength and particle energy. Calculations to date have assumed that the background is constant. We show here, using general plane waves of finite duration, that observables at high quantum nonlinearity scale differently depending on whether intensity or energy is large. At high energy, loop contributions to observables tend to fall with increasing quantum nonlinearity, rather than grow
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