We review the exact analytic solutions of the Klein-Gordon and Dirac equations of a charged particle interacting with a plane electromagnetic radiation field of arbitrary intensity. As basis sets in non-perturbative Furry picture calculations, these quantum states – the Gordon-Volkov states – have long been extensively used in the theoretical study of strong-laser-field matter interactions. The exact analytic solutions for the system of ‘electron plus a quantized radiation mode’ will also be presented. As an illustration, we analyse the high-intensity Compton scattering, resulting in very high-order harmonic radiation and generation of attosecond pulses. The recently found new exact closed-form solutions of the relativistic wave equations in a medium will also be discussed, with an emphasize on their possible relevance in laser acceleration of particles.
 

The infrared catastrophe will be discussed. The Bloch-Nordsieck model which was constructed in 1937 was made to investigate the infrared behaviour of the QED. The model and its solutions will be presented both in zero and finite temperature.
 

We explore Schwinger pair production in rotating time-dependent electric fields using the real-time DHW formalism. We determine the time evolution of the Wigner function as well as asymptotic particle distributions neglecting back-reactions on the electric field. Whereas qualitative features can be understood in terms of effective Keldysh parameters, the field rotation leaves characteristic imprints in the momentum distribution that can be interpreted in terms of interference and multiphoton effects. These phenomena may seed characteristic features of QED cascades created in the antinodes of a high-intensity standing wave laser field.
 

We show that photons subject to a spatially inhomogeneous electromagnetic field experience quantum reflection. This offers the possibility to probe the nonlinearity of the quantum vacuum in the presence of strong electromagnetic fields.
 

Electron-positron pair production in oscillating electric fields is investigated in the nonperturbative threshold regime. Accurate numerical solutions of quantum kinetic theory for corresponding observables are presented and analyzed in terms of a proposed model for an effective mass of electrons and positrons acquired within the given strong electric field. Although this effective mass cannot provide an exact description of the collective interaction of a charged particle with the strong field, physical observables are identified which carry direct and sensitive signatures of the effective mass.
 

The energy range of the planned Very Large Hadron Collider is 100 TeV for p+p collisions, which means 40 ATeV for PbPb reactions. I display a few available predictions on particle production in this energy range, based on different models, including Wigner function description of strong field formation in the initial stage of the heavy collision.
 

We show the recent results on the production of e-e+ or analogously quark-anti quark pairs from strong space-time dependent electric (chromoelectric) fields. The results show that the widely used homogeneous and static string models not just differ from the space-time dependent ones by production rates and predicted spectra but can also be misleading since particles tend to be produced at the interaction surface and not in the volume.
 

Jet flavor probes of Quark Gluon Plasmas produced in nuclear collisions at RHIC/BNL and LHC/CERN test the energy loss dynamics of energetic quark jets propagating through deconfined QCD matter. I review current progress using gravity dual AdS/CFT phenomenology to predict jet observables and compare to recent data and to perturbative QCD (DGLV/CUJET) predictions. This talk is based on work with Andrej Ficnar and Steve Gubser posted on arXiv:1311.6160 [hep-ph] and DOE/JET collaborators, arXiv:1312.5003 [nucl-th].