Photon propagation in slowly varying electromagnetic fields

We study the effective theory of soft photons in slowly varying electromagnetic background fields at one-loop order in QED. This is of relevance for the study of all-optical signatures of quantum vacuum nonlinearity in realistic electromagnetic background fields as provided by high-intensity lasers. The central result derived in this article is a new analytical expression for the photon polarization tensor in two linearly polarized counter-propagating pulsed Gaussian laser beams. As we treat the peak field strengths of both laser beams as free parameters this field configuration can be considered as interpolating between the limiting cases of a purely right- or left-moving laser beam (if one of the peak field strengths is set to zero) and the standing-wave type scenario with two counter-propagating beams of equal strength.Comment: 6 pages, 1 figure; contribution to the Workshop Proceedings of the International Workshop SFP-2016: Strong Field Problems in Quantum Theory, Tomsk, Russia, June 6-12, 201

The photon polarization tensor in a homogeneous magnetic or electric field

We revisit the photon polarization tensor in a homogeneous external magnetic or electric field. The starting point of our considerations is the momentum space representation of the one-loop photon polarization tensor in the presence of a homogeneous electromagnetic field, known in terms of a double parameter integral. Our focus is on explicit analytical insights for both on- and off-the-light-cone dynamics in a wide range of well-specified physical parameter regimes, ranging from the perturbative to the manifestly nonperturbative strong field regime. The basic ideas underlying well-established approximations to the photon polarization tensor are carefully examined and critically reviewed. In particular, we systematically keep track of all contributions, both the ones to be neglected and those to be taken into account explicitly, to all orders. This allows us to study their ranges of applicability in a much more systematic and rigorous way. We point out the limitations of such approximations and manage to go beyond at several instances.Comment: 43 pages, 2 figures; two misprints in Eqs. (118) and (142) corrected (a factor 2^(-2/3) was missing

Quark-antiquark static energy from a restricted Fourier transform

We provide a fully analytical determination of the perturbative quark-antiquark static energy in position space as defined by a restricted Fourier transformation from momentum to position space. Such a determination is complicated by the fact that the static energy genuinely decomposes into a strictly perturbative part (made up of contributions $\sim\alpha_s^n$, with $n\in\mathbb{N}$) which is conventionally evaluated in momentum space, and a so-called ultrasoft part (including terms $\sim\alpha_s^{n+m}\ln^m\alpha_s$, with $n\geq3$ and $m\in\mathbb{N}$) which, conversely, is naturally evaluated in position space. Our approach facilitates the explicit determination of the static energy in position space at the accuracy with which the perturbative potential in momentum space is known, i.e., presently up to order $\alpha_s^4$.Comment: 16 pages, 6 figures; some clarifications added, matches journal versio

Probing vacuum birefringence using x-ray free electron and optical high-intensity lasers

Vacuum birefringence is one of the most striking predictions of strong field quantum electrodynamics: Probe photons traversing a strong field region can indirectly sense the applied "pump" electromagnetic field via quantum fluctuations of virtual charged particles which couple to both pump and probe fields. This coupling is sensitive to the field alignment and can effectively result in two different indices of refraction for the probe photon polarization modes giving rise to a birefringence phenomenon. In this article we perform a dedicated theoretical analysis of the proposed discovery experiment of vacuum birefringence at a x-ray free electron laser/optical high-intensity laser facility. Describing both pump and probe laser pulses realistically in terms of their macroscopic electromagnetic fields, we go beyond previous analyses by accounting for various effects not considered before in this context. Our study facilitates stringent quantitative predictions and optimizations of the signal in an actual experiment.Comment: 23 pages, 4 figure

Photon propagation in slowly varying inhomogeneous electromagnetic fields

Starting from the Heisenberg-Euler effective Lagrangian, we determine the photon current and photon polarization tensor in inhomogeneous, slowly varying electromagnetic fields. To this end, we consider background field configurations varying in both space and time, paying special attention to the tensor structure. As a main result, we obtain compact analytical expressions for the photon polarization tensor in realistic Gaussian laser pulses, as generated in the focal spots of high-intensity lasers. These expressions are of utmost importance for the investigation of quantum vacuum nonlinearities in realistic high-intensity laser experiments.Comment: 15 pages, 1 figure; some clarifications added, matches journal versio

Probing vacuum polarization effects with high-intensity lasers

These notes provide a pedagogical introduction to the theoretical study of vacuum polarization effects in strong electromagnetic fields as provided by state-of-the-art high-intensity lasers. Quantum vacuum fluctuations give rise to effective couplings between electromagnetic fields, thereby supplementing Maxwell’s linear theory of classical electrodynamics with nonlinearities. Resorting to a simplified laser pulse model, allowing for explicit analytical insights, we demonstrate how to efficiently analyze all-optical signatures of these effective interactions in high-intensity laser experiments. Moreover, we highlight several key features relevant for the accurate planning and quantitative theoretical analysis of quantum vacuum nonlinearities in the collision of high-intensity laser pulses