Abstract
Analytical calculations of radiative corrections in strong-field QED have hinted that in the presence of an intense plane wave the effective coupling of the theory in the high-energy sector may increase as the $(2/3)$-power of the energy scale. These findings have raised the question of their compatibility with the corresponding logarithmic increase of radiative corrections in QED in vacuum. However, all these analytical results in strong-field QED have been obtained within the limiting case of a background constant crossed field. Starting from the polarization operator and the mass operator in a general plane wave, we show that the constant-crossed-field limit and the high-energy limit do not commute with each other and identify the physical parameter discriminating between the two alternative limits orders. As a result, we find that the power-law scaling at asymptotically large energy scales pertains strictly speaking only to the case of a constant crossed background field, whereas high-energy radiative corrections in a general plane wave depend logarithmically on the energy scale as in vacuum. However, we also confirm the possibility of testing the ``power-law'' regime experimentally by means of realistic setups involving, e.g., high-power lasers or high-density electron-positron bunches.
Highlights
The predictions of QED agree with experiments with astonishing accuracy
The physical relevance of the RN conjecture is broadened by the so-called local constant field limit, stating that in the limit of low-frequency plane waves the probabilities of QED processes reduce to the corresponding probabilities in a constant crossed field (CCF) averaged over the phase-dependent plane-wave profile [14]
Since for sufficiently large values of θ0, the parameter r0 1⁄4 ξ20=θ0 introduced above will be at a certain point smaller than unity, we can conclude that the polarization operator in a plane wave features a logarithmic behavior in the high-energy limit
Summary
The predictions of QED agree with experiments with astonishing accuracy (see, e.g., Refs. [1,2]). About the high-energy behavior of radiative corrections in strong-field QED in a constant crossed field (CCF) The physical relevance of the RN conjecture is broadened by the so-called local constant field limit, stating that in the limit of low-frequency plane waves the probabilities of QED processes reduce to the corresponding probabilities in a CCF averaged over the phase-dependent plane-wave profile [14]. The aim of the present work is to show that the highenergy limit and the low-frequency limit do not commute with each other and that the power-law scaling of the effective coupling constant at asymptotically large energy scales strictly speaking pertains only to the CCF background field. Operator, respectively, appeared in Ref. [36], whose conclusions are in agreement with ours
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