Abstract
As a toy model for QED in strong background fields, we consider the impact of back-reaction and loop effects on scattering processes in quantum optics. We show that neglecting back-reaction misses qualitative and quantitative features of strong-field physics. We are able to study an analogue of the Narozhny-Ritus conjecture on the scaling of higher loop diagrams with intensity: we prove that there is no corresponding behaviour in our model. Implications for QED are identified and discussed.
Highlights
Dividing a system into a fixed background, and perturbations around it, is a standard and fruitful approach in many areas of physics
The expansion parameter is the usual, small, coupling, but where the background is treated exactly at each order. It has been conjectured, based on the scaling of certain higher loop diagrams in plane waves, see Fig. 1, that the effective coupling parameter in the Furry picture is dependent on a power of the background field strength [19]
This would imply a breakdown of perturbative methods, or of the background field approximation, at sufficiently high intensity, and necessitate an allorders resummation of Furry picture Feynman diagrams
Summary
Dividing a system into a fixed background, and perturbations around it, is a standard and fruitful approach in many areas of physics. The expansion parameter is the usual, small, coupling, but where the background is treated exactly at each order It has been conjectured, based on the scaling of certain higher loop diagrams in plane waves, see Fig. 1, that the effective coupling parameter in the Furry picture is dependent on a (positive) power of the background field strength [19]. The model has the advantages that it is exactly solvable, and that its three-point vertex mimics that of QED, allowing an analogy with Feynman diagrams While this is certainly a gross simplification of QED, single-mode models commonly reveal new physics and offer methods of including explicit quantum corrections which are otherwise hard to capture [29,30,31,32].
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