In the calculation of probabilities of physical processes occurring in a background classical field, the local constant field approximation (LCFA) relies on the possibility of neglecting the space-time variation of the external field within the region of formation of the process. This approximation is widely employed in strong-field QED as it allows to evaluate probabilities of processes occurring in arbitrary electromagnetic fields starting from the corresponding quantities computed in a constant electromagnetic field. Here, we scrutinize the validity of the LCFA in the case of nonlinear Compton scattering focusing on the role played by the energy of the emitted photon on the formation length of this process. In particular, we derive analytically the asymptotic behavior of the emission probability per unit of photon light-cone energy k− and show that it tends to a constant for k− → 0. With numerical codes being an essential tool for the interpretation of present and upcoming experiments in strong-field QED, we obtained an improved approximation for the photon emission probability, implemented it numerically, and showed that it amends the inaccurate behavior of the LCFA in the infrared region, where it remains in qualitative and good quantitative agreement with the full strong-field QED probability.PACS numbers: 12.20.Ds, 41.60.-m arXiv:1708.08276v3 [hep-ph]

We demonstrate the experimental feasibility of probing the fully nonperturbative regime of quantum electrodynamics with a 100 GeV-class particle collider. By using tightly compressed and focused electron beams, beamstrahlung radiation losses can be mitigated, allowing the particles to experience extreme electromagnetic fields. Three-dimensional particle-in-cell simulations confirm the viability of this approach. The experimental forefront envisaged has the potential to establish a novel research field and to stimulate the development of a new theoretical methodology for this yet unexplored regime of strong-field quantum electrodynamics.The interaction of light and matter is governed by quantum electrodynamics (QED), which is the most successfully tested theory in physics. According to the present understanding of QED, the properties of matter change qualitatively in the presence of strong electromagnetic fields. The importance of strong-field quantum effects is determined by the Lorentz invariant parameter χ = E * /E cr [1, 2] (also called beamstrahlung parameter in the context of particle colliders), which compares the electromagnetic field in the electron/positron rest frame E * with the QED critical field E cr = m 2 c 3 /(e ) ≈ 1.32×10 18 V/m. Here, m and e are the electron/positron mass and charge, c is speed of light, and is reduced Planck constant, respectively. Whereas classical electrodynamics is valid if χ 1, quantum effects like the recoil of emitted photons (quantum radiation reaction) and the creation of matter from pure light become important in the regime χ 1. Eventually, the interaction between light and matter becomes fully nonperturbative if χ 1. The behavior of matter near QED critical field strengths (i.e., the regime χ ∼ 1) is important in astrophysics (e.g., gamma-ray bursts, pulsar magnetosphere, supernova explosions) [3][4][5], at the interaction point of future linear particle colliders [6][7][8][9][10][11][12][13], and in upcoming high energy density physics experiments, where laserplasma interactions will probe quantum effects [14]. Experimental investigations of strong-field QED have just approached χ 1, e.g., by combining highly energetic particles with intense optical laser fields. This experimental scheme, first realized in the SLAC E-144 experiment [15,16], has been recently revisited [17,18]. Notable alternatives are x-ray free electron lasers [19], highly charged ions [20], heavy-ion collisions [21], and strong crystalline fields [22]. The success of QED in the regime χ 1 is based on the smallness of the fine-structure *

The local-constant-field approximation (LCFA) is an essential theoretical tool for investigating strong-field QED phenomena in background electromagnetic fields with complex spacetime structure. In our previous work [Phys. Rev. A 98, 012134 (2018)] we have analyzed the shortcomings of the LCFA in nonlinear Compton scattering at low emitted photon energies for the case of a background plane-wave field. Here, we generalize that analysis to background fields, which can feature a virtually arbitrary spacetime structure. In addition, we provide an explicit and simple implementation of an improved expression of the nonlinear Compton scattering differential probability that solves the main shortcomings of the standard LCFA in the infrared region, and is suitable for background electromagnetic fields with arbitrary spacetime structure such as those occurring in particle-in-cell simulations. Finally, we carry out a systematic procedure to calculate the probability of nonlinear Compton scattering per unit of emitted photon light-cone energy and of nonlinear Breit-Wheeler pair production per unit of produced positron light-cone energy beyond the LCFA in a plane-wave background field, which allows us to identify the limits of validity of this approximation quantitatively.

Short-pulse effects are investigated for the nonlinear Breit-Wheeler process, i.e. the production of an electron-positron pair induced by a gamma photon inside an intense plane-wave laser pulse. To obtain the total pair-creation probability we verify (to leading-order) the cutting rule for the polarization operator in the realm of strong-field QED by an explicit calculation. Using a doubleintegral representation for the leading-order contribution to the polarization operator, compact expressions for the total pair-creation probability inside an arbitrary plane-wave background field are derived. Correspondingly, the photon wave function including leading-order radiative corrections in the laser field is obtained via the Schwinger-Dyson equation in the quasistatic approximation. Moreover, the influence of the carrier-envelope phase (CEP) and of the laser pulse shape on the total pair-creation probability in a linearly polarized laser pulse is investigated, and the validity of the (local) constant-crossed field approximation analyzed. It is shown that with presently available technology pair-creation probabilities of the order of ten percent could be reached for a single gamma photon.

We derive an alternative representation of the leading-order contribution to the polarization operator in strong-field quantum electrodynamics with a plane-wave electromagnetic background field, which is manifestly symmetric with respect to the external photon momenta. Our derivation is based on a direct evaluation of the corresponding Feynman diagram, using the Volkov representation of the dressed fermion propagator. Furthermore, the validity of the Ward-Takahashi identity is shown for general loop diagrams in an external plane-wave background field.