In memory of Efim Samoilovich Fradkin

Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity

“…The matter is that there is an instability of the magnetic field reflected in appearance of imaginary part of the effective Lagrangian (already for magnetic-like case under consideration) due to contribution of unstable gluon mode in a magnetic field [24] into the spectral decomposition of the effective action. (The presence of the imaginary part not seen in [7] may be reproduced [25], [9] also in calculations following the Schwinger's proper time technique). This instability is known to be resolved by going out of the sector of covariantly-constant fields.…”

“…In Subsection C we inspect two one-loop Lagrangians that are known to produce spontaneous magnetic fields. One of them [7] relates to the Yang-Mills theory taken against the uniform background formed by a constant chromomagnetic field directed along a single isotopic direction. The other [8] is a one-loop Lagrangian of electromagnetic field in interaction with a complex massless scalar field taken in de Sitter space.…”

Generalized eikonal approximation for strong-field ionization

“…For nonrelativistic case the dipole approximation for the laser pulse was used and applied to free-free transitions, whereas for the relativistic one the finite, in general, laser pulses in the plane-wave fronted approximation were considered. Note that the approach developed by Kamiński in [11] was based on the proper-time method, which for propagators in quantum theories was proposed by Fock [12], and further developed by Schwinger [13,14], and by Fradkin and co-workers [15][16][17] (see also the review [18]). It has been demonstrated that, for potential scattering in the presence of strong fields, the EA has certain limitations.…”