Photon pair creation in intense magnetic fields

Abstract

The vacuum polarization of photons in intense, homogeneous magnetic fields is recalculated, using a proper-time method presented by Schwinger. This result is applied to compute exactly, in closed form, the photon absorption coefficient due to pair creation, ${k}_{\ensuremath{\parallel},\ensuremath{\perp}}$, corresponding to the polarization of the photon parallel or perpendicular to the plane of the photon momentum $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ and the homogeneous magnetic field $\stackrel{\ensuremath{\rightarrow}}{H}$. Specializing this general expression to the high-frequency, weak-field limit yields ${k}_{\ensuremath{\parallel},\ensuremath{\perp}}(\ensuremath{\omega})=\frac{1}{2}\ensuremath{\alpha}sin\ensuremath{\theta} {\ensuremath{\omega}}_{H}\frac{4\sqrt{3}}{\ensuremath{\lambda}\ensuremath{\pi}}\ensuremath{\int}{0}^{1}\frac{\mathrm{dv}}{1\ensuremath{-}{v}^{2}}[{(1\ensuremath{-}\frac{1}{3}{v}^{2})}_{\ensuremath{\parallel}},{(\frac{1}{2}+\frac{1}{6}{v}^{2})}_{\ensuremath{\perp}}]{K}_{\frac{2}{3}}\left(\frac{4}{\ensuremath{\lambda}(1\ensuremath{-}{v}^{2})}\right),$where $|\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}|=\ensuremath{\omega}$, $\ensuremath{\lambda}=\frac{3}{2}(\frac{eH}{{m}^{2}})(\frac{\ensuremath{\omega}}{m})sin\ensuremath{\theta}$, ${\ensuremath{\omega}}_{H}=\frac{eH}{m}$, and $\ensuremath{\theta}$ is the angle between $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ and $\stackrel{\ensuremath{\rightarrow}}{H}$. Comparing this expression with those obtained in the prior computations, we find that ours is more compact and much simpler in form and that ours is a simplied version of theirs.