Magnetic response from constant backgrounds to Coulomb sources

Within general nonlinear electrodynamics given by a local action, very special magnetic field configuration carrying no magnetic charge is found as a linear response of the vacuum, filled with constant electric and magnetic fields, to an embedded static electric charge. When the electric charge is point-like and external fields are parallel, the response found may be interpreted as a field of two point-like magnetic charges of opposite polarities in one point. Coefficients characterizing the magnetic response and induced current are specialized to quantum electrodynamics (QED), where the nonlinearity is taken as that determined by the local Heisenberg–Euler effective action. It is demonstrated how the same response is reproduced in the (nonisotropic) region remote from the charge by considering the polarization operator of QED.