Light propagation effects in QED: Effective action approach

The effects of light propagation in constant magnetic and electric backgrounds are considered in the framework of the effective action approach. We use the exact analytic series representation for the one-loop effective action of QED and apply it to the birefringence effect. Analytical results for the light velocity modes are obtained for the weak and the strong field regime. We present asymptotic formulas for the light velocity modes for the ultrastrong magnetic field which can be realized in some neutron stars.

Figure 1

Light velocity in the plane orthogonal to the magnetic field: (i) exact one-loop approximated result; (ii) result in the weak field approximation. The magnetic field strength $a$ is measured in units of electron mass $m^2$.

Figure 2

Light velocity in the orthogonal plane to the electric field: (i) the exact one-loop approximated result; (ii) the result obtained in weak field approximation. The electric field strength $b$ is given in units of electron mass $m^2$.

Figure 3

The upper curve, (ii), corresponds to the $\parallel$ mode and the lower one, (i), corresponds to the $\perp$ mode. This can be compared with the light velocity averaged over polarizations, curve (iii).

Figure 4

Light velocity in the electric field for the $\parallel$ mode, (i), and for the $\perp$ mode, (ii).