Finite-field QED corrections to vacuum birefringence and magnetar polarization transport

Abstract We study low-energy photon propagation in a constant magnetic field within the finite-field one-loop Heisenberg–Euler framework and apply the resulting mode-dependent refractive indices to magnetar polarization transport. In a centered-dipole model, the polarization-limiting radius is unchanged to better than $$10^{-12}$$ 10 - 12 because mode decoupling occurs at $$\sim 10^2R_\textrm{NS}$$ ∼ 10 2 R NS , where $$B\ll B_\textrm{cr}$$ B ≪ B cr . Near the surface, however, the weak-field Cotton–Mouton expression overestimates the accumulated birefringent phase by up to a factor 2.9 at $$10^{15}$$ 10 15 G. At the plasma–vacuum resonance, finite-field corrections reduce the resonance density by $$32\%$$ 32 % and raise the adiabatic conversion energy by $$14\%$$ 14 % for 1E 1547.0-5408; the corresponding changes are factors 2.6 and 1.37 for 1RXS J1708-4009, and factors 9.7 and 2.13 for SGR 1806-20, the latter controlled by the strong-field asymptote. The parallel-mode magnetic response remains positive and exhibits a broad maximum near $$17B_\textrm{cr}$$ 17 B cr . Its strict $$\mathcal O(\alpha )$$ O ( α ) expansion is monotonic, indicating that the detailed position and profile of the maximum are not controlled beyond the present approximation and require higher-loop assessment. These results identify vacuum-resonance observables as the most sensitive channel for testing finite-field QED in magnetars.