Nonlinear magnetic response of the magnetized vacuum to applied electric field

We find first nonlinear correction to the field, produced by a static charge at rest in a background constant magnetic field. It is quadratic in the charge and purely magnetic. The third-rank polarization tensor - the nonlinear response function - is written within the local approximation of the effective action in an otherwise model- and approximation-independent way within any P-invariant nonlinear electrodynamics, QED included.Comment: 11 pages without figures or tables. Numerical coefficients and some signs in Version I corrected, three new references and two equations adde

Finite field-energy of a point charge in QED

We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, which possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly solved in the class of static central-symmetric electric fields. Collation with quantum electrodynamics (QED) results in the total field energy about twice the electron mass. The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler-Heisenberg local Lagrangian in QED in powers of the field strenth

When electric charge becomes also magnetic

In nonlinear electrodynamics, QED included, we find a static solution to the field equations with an electric charge as its source, which is comprised of homogeneous parallel magnetic and electric fields, and a radial spherically-nonsymmetric long-range magnetic field, whose magnetic charge is proportional to the electric charge and also depends on the homogeneous component of the solution.Comment: Four pages, no figure

Interaction between two point-like charges in nonlinear electrostatics

We consider two point-like charges in electrostatic interaction within the framework of a nonlinear model, associated with QED, that provides finiteness of their field energy. We find the common field of the two charges in a dipole-like approximation, where the separation between them R is much smaller than the observation distance r : with the linear accuracy with respect to the ratio R / r, and in the opposite approximation, where R≫r, up to the term quadratic in the ratio r / R. The consideration proposes the law a+bR1/3 for the energy, when the charges are close to one another, R→0 . This leads to the singularity of the force between them to be R−2/3 , which is weaker than the Coulomb law, R−2

QED with external field: Hamiltonian treatment for anisotropic medium formed by the Lorentz-non-invariant vacuum

Nonlinear electrodynamics, QED included, is considered against the Lorentz-noninvariant external field background, treated as an anisotropic medium. Hamiltonian formalism is applied to electromagnetic excitations over the background, and entities of electrodynamics of media, such as field inductions and intensities, are made sense of in terms of canonical variables. Both conserved and nonconserved generators of space-time translations and rotations are defined on the phase space, and their Hamiltonian equations of motion and Dirac bracket relations, different from the Poincar\'e algebra, are established. Nonsymmetric, but--in return--gauge-invariant, energy-momentum tensor suggests a canonical momentum density other than the Poynting vector. A photon magnetic moment is found to govern the evolution of the photon angular momentum. It is determined by the antisymmetric part of the energy-momentum tensor.Comment: 28 page