Advances in QED with intense background fields

TL;DR

The paper surveys advances in quantum electrodynamics under intense background fields, focusing on nonperturbative Schwinger physics, higher-order processes, and realistic laser-pulse modeling across the last decade. It consolidates the Furry-picture framework, plane-wave and beyond-plane-wave backgrounds, and a spectrum of first- and second-order processes, highlighting advances in approximation schemes (LCFA, LMA, saddle-point methods) and resummation techniques (chi-expansions, Mueller matrices). It also discusses light-by-light scattering, Schwinger pair creation, and the Ritus–Narozhny conjecture, extending the discussion to higher-order corrections, back-reaction, and potential connections to beyond-Standard-Model physics. The review emphasizes experimental relevance with upcoming facilities like multi-PW lasers and LUXE, and outlines theoretical challenges, including strong-field resummation, non-plane-wave backgrounds, and consistent treatment of backreaction and cascades. Overall, it frames SFQED as a robust, cross-disciplinary field at the intensity frontier with implications for fundamental physics and potential laboratory probes of new physics.

Abstract

Upcoming and planned experiments combining increasingly intense lasers and energetic particle beams will access new regimes of nonlinear, relativistic, quantum effects. This improved experimental capability has driven substantial progress in QED in intense background fields. We review here the advances made during the last decade, with a focus on theory and phenomenology. As ever higher intensities are reached, it becomes necessary to consider processes at higher orders in both the number of scattered particles and the number of loops, and to account for non-perturbative physics (e.g. the Schwinger effect), with extreme intensities requiring resummation of the loop expansion. In addition to increased intensity, experiments will reach higher accuracy, and these improvements are being matched by developments in theory such as in approximation frameworks, the description of finite-size effects, and the range of physical phenomena analysed. Topics on which there has been substantial progress include: radiation reaction, spin and polarisation, nonlinear quantum vacuum effects and connections to other fields including physics beyond the Standard Model.

Figures (38)

• Figure 1: Indicative bibliometric search using NASA-ADS, for at least one of the following terms occurring in the abstract: "strong field QED", "nonlinear QED", "nonlinear Compton", "nonlinear Breit-Wheeler", "locally constant field", "Schwinger effect", "Schwinger pair". The shaded region is the last decade, on which the current review is focussed.
• Figure 2: Laser-particle experiments. Solid lines and markers indicate reported experimental results; dashed lines and empty markers indicate planned experiments. The specific experimental values plotted, in $(\xi,\eta)$ co-ordinates, are: Apollon papadopoulos2016; ATLAS-MPQ $(0.9,5\ldots 6\times 10^{-4})$2015PhRvL.114s5003K; BNL-ATF $(0.6, 7.5\times10^{-4})$Sakai:2015mra; CALA 2021NJPh...23j5002S; CoReLS 2021Optic...8..630Y; DIOCLES$^1$$(0.4,0.0029)$Chen:2013mba; DIOCLES$^2$$(2\ldots12,0.0036)$Yan2017; DRACO $(0.6,0.0027~[230\,\textrm{MeV}])$Hannasch:2021kyh; E144 $(0.36,0.83)$Bamber:1999zt; E320 $(2,0.15)$Salgado:2021fgt; E320$^{\textsf{II}}$ (proposed upgrade) $(16,0.15)$meuren2019probing; ELI Turcu:2016dxm; EP-OPAL Zuegel:14; Gemini$^{1}$$(1\ldots2,0.006)$Sarri:2014gea; Gemini$^{2}$$(24.7,0.003\ldots0.02)$Cole:2017zcaPoder:2017dpw; LUXE 0 $(0.1\ldots5,0.13\ldots0.19)$Abramowicz:2021zja; LUXE 1 $(5\ldots20,0.10\ldots0.19)$Abramowicz:2021zja; VULCAN Hernandez_Gomez_2010; SEL sel18; SULF Li:18; XCELS Mukhin_2021; ZEUS Nees21. The grey 'Multi-PW Class' and 'Multi-10PW Class' regions correspond to typical values of $\xi$ that can be produced at these laser facilities, and values of $\eta$ correspond to $1\ldots5\,\textrm{GeV}$ particle beams colliding at 20 degrees with the laser pulse, naïvely assuming the electron reaches the peak intensity at the focus of the laser pulse.
• Figure 3: In a background field, the Feynman rules are formulated in position space, due to the general loss of overall momentum conservation. The fermion propagator $S(x,y)$ (left) is the inverse of the Dirac operator in the background, i.e. obeys (\ref{['eq:DiracBG']}), and is represented by a double line. The lack of translation invariance means that the propagator is a function of both the spacetime coordinates which it connects. The vertex (middle) and photon propagator (right) are as in QED without background.
• Figure 4: The diagrammatic expansion of the Furry picture propagator in terms of ordinary (position space) Feynman diagrams in vaccum; each external photon line represents an interaction with the external field via the usual vertex $-ie\mathcal{A}_\mu \gamma^\mu$.
• Figure 5: A pulse of light moving in the negative $z$-direction, modelled as a plane wave of finite duration, is shown as the red region. The plane wave is homogeneous and infinitely extended in the transverse directions (not shown). All massive particles, see the blue tracks, enter and leave the wave at the same lightfront times $x^{ +}_1$ and $x^{ +}_2$ respectively, though these can correspond to different $t$ and $z$. Figure taken from Seipt:2017ckc.