Photon decay into neutrinos in a strong magnetic field

The real photon decay, $\gamma \to \nu \overline{\nu }$, is calculated in strong magnetic fields ($H\sim {10}^{13}$ G) using a version of Schwinger's mass operator technique, which makes use of the explicit form of the electron Green's function. The reaction is kinematically allowed by an index of refraction less than one. This latter condition may arise either from quantum electrodynamics (high frequencies) or from the effects of a material medium or plasma (low frequencies). The calculation is based on point charged- and neutral-current interactions for the leptons, which should agree with an S${\mathrm{U}}_2$ ${\times \mathrm{U}}_1$ gauge-theory calculation as long as $\frac{\omega }{m_W}$ and $\frac{\mathrm{eH}}{{m_W}^2}$ are both small compared to unity (where $\omega$ is the photon frequency and $m_W$ is the mass of the $W$ boson). Numerical results for the absorption coefficient and energy loss rate are given, since the mechanism may be important in the astrophysics of neutron stars.