Physics in Ultra-strong Magnetic Fields
  In magnetic fields stronger than B_Q = 4.4 X 10^13 Gauss, an electron's Landau excitation energy exceeds its rest energy. I review the physics of this strange regime and some of its implications for the crusts and magneto- spheres of neutron stars. In particular, I describe how ultra-strong fields   >> render the vacuum birefringent and capable of distorting and magnifying images ("magnetic lensing");   >> change the self-energy of electrons: as B increases they are first slightly lighter than $m_e$, then slightly heavier;   >> cause photons to rapidly split and merge with each other;   >> distort atoms into long, thin cylinders and molecules into strong, polymer-like chains;   >> enhance the pair density in thermal pair-photon gases; >> strongly suppress photon-electron scattering, and >> drive the vacuum itself unstable, at extremely large B.   In a concluding section, I discuss recent observations of the spindown histories of soft gamma repeaters and anomalous X-ray pulsars. The magnetar model gives a promising framework for understanding these data. 
Robert C. Duncan