STABILITY AND INSTABILITY OF RELATIVISTIC ELECTRONS IN CLASSICAL ELECTROMAGNETIC-FIELDS

The stability of matter composed of electrons and static nuclei is inv estigated for a relativistic dynamics for the electrons given by a sui tably projected Dirac operator and with Coulomb interactions. In addit ion there is an arbitrary classical magnetic field of finite energy. D espite the previously known Facts that ordinary nonrelativistic matter with magnetic fields, or relativistic matter without magnetic fields, is already unstable when alpha, the fine structure constant, is too l arge, it is noteworthy that the combination of the two is still stable provided the projection onto the positive energy states of the Dirac operator, which defines the electron, is chosen properly. A good choic e is to include the magnetic field in the definition. A bad choice, wh ich always leads to instability, is the usual one in which the positiv e energy states are defined by the free Dirac operator. Both assertion s are proved here.