STABILITY OF RELATIVISTIC MATTER WITH MAGNETIC-FIELDS

Stability of matter with Coulomb forces has been proved for nonrelativ istic dynamics, including arbitrarily large magnetic fields, and for r elativistic dynamics without magnetic fields. In both cases stability requires that the fine structure constant alpha be not too large. It w as unclear what would happen for both relativistic dynamics and magnet ic fields, or even how to formulate the problem clearly. We show that the use of the Dirac operator allows both effects, provided the filled negative energy ''sea'' is defined properly. The use of the free Dira c operator to define the negative levels leads to catastrophe for any alpha, but the use of the Dirac operator with magnetic field leads to stability.