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We propose a model to account for the bursts from soft gamma repeaters (SGRs)and anomalous X-ray pulsars (AXPs) in which quantum electrodynamics (QED) playsa vital role. In our theory, that we term ``fast-mode breakdown,''magnetohydrodynamic (MHD) waves that are generated near the surface of aneutron star and propagate outward through the magnetosphere will be modifiedby the polarization of the vacuum. For neutron star magnetic fields$B_\rmscr{NS} \gtrsim B_\rmscr{QED} \approx 4.4 \times 10^{13}$ G, theinteraction of the wave fields with the vacuum produces non-linearities in fastMHD waves that can steepen in a manner akin to the growth of hydrodynamicshocks. Under certain conditions, fast modes can develop field discontinuitieson scales comparable to an electron Compton wavelength, at which point the waveenergy will be dissipated through electron-positron pair production. We showthat this process operates if the magnetic field of the neutron star issufficiently strong and the ratio of the wavelength of the fast mode to itsamplitude is sufficiently small, in which case the wave energy will beefficiently converted into an extended pair-plasma fireball. The radiativeoutput from this fireball will consist of hard X-rays and soft $\gamma$-rays,with a spectrum similar to those seen in bursts from SGRs and AXPs (abridged).Comment: 28 pages, 5 figures, accepted by ApJ, minor changes to reflect  accepted versio

A QED Model for the Origin of Bursts from Soft Gamma Repeaters and Anomalous X‐Ray Pulsars