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In light of the conference Quantum Mathematical Physics held in Regensburg in 2014, we give our perspective on the external field problem in quantum electrodynamics (QED), i.e., QED without photons in which the sole interaction stems from…
The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial…
A quantum kinetic equation has been derived for the description of pair production in a time-dependent homogeneous electric field $E(t)$. As a source term, the Schwinger mechanism for particle creation is incorporated. Possible particle…
We investigate a two-component, cylindrical, quasi-one-dimensional quantum plasma subjected to a {\em radial} confining harmonic potential and an applied magnetic field in the symmetric gauge. It is demonstrated that such a system as can be…
The Schwinger mechanism of electron-positron pair production in the presence of strong external electric fields is analyzed numerically for the case of one- and two-dimensional field configurations where the external field depends both on…
Electron-positron pair production by the superposition of two laser pulses with different frequencies and amplitudes is analyzed as a particular realization of the assisted dynamic Schwinger effect. It is demonstrated that, within a…
We study particle creation in a single pulse of an electric field in scalar quantum electrodynamics. We first identify parameter regions of the theory where the dynamical pair creation and Schwinger mechanism respectively dominate each…
We have developed new methods to calculate dispersion curves (analytically in the simpler cases) from which we are able to derive the spatial distribution of electron and current densities. We investigate the case where the magnetic field…
The behavior of a classical charged point particle under the influence of only a Coulombic binding potential and classical electromagnetic zero-point radiation, is shown to yield agreement with the probability density distribution of…
Modern laser systems are able to generate short and intense laser pulses ionizing matter in the poorly explored barrier-suppression regime. Field ionization in this regime is studied analytically and numerically. For analytical studies,…
We study quantum electrodynamics (QED) in the light-front dynamical form by using null-plane causal perturbation theory. We establish the equivalence with instant dynamics for the scattering processes, whose normalization allows to…
The electric current conservation in a two-dimensional quantum wire under a time dependent field is investigated. Such a conservation is obtained as the global density of states contribution to the emittance is balanced by the contribution…
We introduce a complex-extended continuum level density and apply it to one-dimensional scattering problems involving tunneling through finite-range potentials. We show that the real part of the density is proportional to a real "time…
The Schr\"odinger-Pauli theory of electrons in the presence of a static electromagnetic field can be described from the perspective of the individual electron via its equation of motion or `Quantal Newtonian' first law. The law is in terms…
Converging cylindrical electromagnetic fields in vacuum have been shown (E. I. Zababakhin, M. N. Nechaev, {\it Soviet Physics JETP}, {\bf 6}, 345 (1958)) to exhibit amplitude "cumulation". It was found that the amplitude of self-similar…
We consider the emission spectrum of high-energy electrons in an intense laser field. At high intensities ($a_0\sim200$) we find that the QED theory predicts a narrower angular spread of emissions than the classical theory. This is due to…
We consider a statistical ensemble of particles of mass m, which can be described by a probability density \rho and a probability current \vec{j} of the form \rho \nabla S/m. The continuity equation for \rho and \vec{j} implies a first…
Classically, electromagnetic pulses are described by real fields that couple to charged matter and propagate causally. We will show here that real fields of the form used in standard classical electromagnetic theory have a quantum…
It is a long-standing non-trivial prediction of quantum electrodynamics that its vacuum is unstable in the background of a static, spatially uniform electric field and, in principle, sparks with spontaneous emission of electron-positron…
Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that,…