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We consider Sauter-Schwinger pair production by electric fields that depend on both time and space, E(t; z) and E(t; x; y). For space independent fields E(t), momentum conservation δ(p + p') fixes the positron momentum p' in terms of the electron momentum p. For E(t; z), on the other hand, pz and pź are independent. However, previous exact-numerical studies have considered only the probability as a function of a single momentum variable, P(pz), P(pź) or P(pź − pz), but not the correlation P(pz; pź). In this paper, we show how to obtain P(pz; pź) by solving the Dirac equation numerically. To do so, we split the wave function into a background and a scattered wave, ψ(t; x) = ψback:(t; x) + ψscat:(t; x), where ψback: ∝ exp(±ipx + gauge term). ψscat. vanishes outside a past light cone and is obtained by solving (i= D − m)ψscat: = −(i= D − m)ψback:. backward in time starting with ψscat:(t → +∞; x) = 0.

We consider nonlinear trident, e− → e−e−e+, in various electric background fields. This process has so far been studied for plane-wave backgrounds, using Volkov solutions. Here we first use WKB for trident in time-dependent electric fields, and then for fields which vary slowly in space. Then we show how to use worldline instantons for more general fields which depend on both time and space. For time-dependent fields the WKB approach is at least as simple to use as the worldline approach, but already the relatively modest step of including a slow spatial dependence makes the worldline approach much more efficient.

We use a worldline-instanton formalism to study the momentum spectrum of Schwinger pair production in spacetime fields with multiple stationary points. We show that the interference structure changes fundamentally when going from purely time-dependent to space-time-dependent fields. For example, it was known that two time-dependent pulses give interference if they are antiparallel, i.e., (Formula presented), but here we show that two spacetime pulses will typically give interference if they instead are parallel, i.e., (Formula presented). We take into account the fact that the momenta of the electron, pz, and of the positron, p0z, are independent for (Formula presented) [it would be (Formula presented)], and find a type of fields which give moiré patterns in the pz − p0z plane. Depending on the separation of the two pulses, we also find an Aharonov-Bohm phase. We also study complex momentum saddle points in order to obtain the integrated probability from the spectrum. Finally, we calculate an asymptotic expansion for the eigenvalues of the Sturm-Liouville equation that corresponds to the saddle-point approximation of the worldline path integral, use that expansion to compute the product of the eigenvalues, and compare this with the result obtained with the Gelfand-Yaglom method.

We show how to use a worldline-instanton formalism to calculate, to leading order in the weak-field expansion, the momentum spectrum of nonlinear Breit-Wheeler pair production in fields that depend on time and one spatial coordinate. We find a nontrivial dependence on the width, lambda, of the photon wave packet, and the existence of a critical point lambda(c). For lambda < lambda(c) and a field with one peak, the spectrum has one peak where the electron and positron have the same energy. For lambda > lambda(c) c this splits into two peaks. We calculate a high-energy (Omega >> 1 ) expansion, which to leading order agrees with the results obtained by replacing the spacetime field with a plane wave and using the well-known Volkov solutions. We also calculate an expansion for Omega similar to a(0) >> 1 , where the field is strong enough to significantly bend the trajectories of the fermions despite Omega >> 1.

We calculate the momentum spectrum of electron-positron pairs created via the Schwinger mechanism by a class of four-dimensional electromagnetic fields called e-dipole fields. To the best of our knowledge, this is the first time the momentum spectrum has been calculated for 4D, exact solutions to Maxwell's equations. Moreover, these solutions give fields that are optimally focused, and are hence particularly relevant for future experiments. To achieve this we have developed a worldline instanton formalism where we separate the process into a formation and an acceleration region.

We derive analytical χ≪1 approximations for spin-dependent quantum radiation reaction for locally constant and locally monochromatic fields. We show how to factor out fast spin oscillations and obtain the degree of polarization in the plane orthogonal to the magnetic field from the Frobenius norm of the Mueller matrix. We show that spin effects lead to a transseries in χ, with powers χ^k, logarithms (ln χ)^k, and oscillating terms, coso(.../χ) and sin (.../χ). In our approach we can obtain each moment, <(kP)^m>, of the light-front longitudinal momentum independently of the other moments and without considering the spectrum. We show how to obtain a low-energy expansion of the spectrum from the moments by treating m as a continuous, complex parameter and performing an inverse Mellin transform. We also show how to obtain the spectrum, without making a low-energy approximation, from a handful of moments using the principle of maximum entropy.

In previous works we derived equations for the average momentum of high-energy electrons experiencing quantum radiation reaction in strong electromagnetic plane-wave background fields. In this paper we derive similar equations for the momentum spectrum. We formulate the equations in terms of the cumulative function and study the relation between the equations for the spectrum and the equations for the moments, analyze the structure of the low-energy expansions, and finally explain how our formulation is essentially in terms of a "Green's function"which allows us to study the dynamics without choosing a specific initial wave packet (or particle-bunch distribution).

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.

Strong field physics close to or above the Schwinger limit are typically studied with vacuum as initial condition or by considering test particle dynamics. However, with a plasma present initially, quantum relativistic mechanisms such as Schwinger pair creation are complemented by classical plasma nonlinearities. In this work we use the Dirac-Heisenberg-Wigner formalism to study the interplay between classical and quantum mechanical mechanisms in the regime of ultrastrong electric fields. In particular, the effects of initial density and temperature on the plasma oscillation dynamics are determined. Finally, comparisons with competing mechanisms such as radiation reaction and Breit-Wheeler pair production are made.

We show how to resum the Furry-picture α expansion in order to take quantum radiation reaction and spin transition into account in the nonlinear trident process in (pulsed) plane-wave background fields. The results are therefore nontrivial functions of both the background field strength, eE, and the coupling to the quantized photon field, α=e2/4π. The effective expansion parameter, T, is α times eE/mω≫1, which makes higher orders in α important. We show that they can change the sign of the spin-dependent part already at T<1, which will be experimentally accessible. We also present a new resummation method that essentially does to a convergent series what Borel-Padé resummation does to an asymptotic series.