E.H. Lieb, H. Siedentop, J.P. Solovej
Stability of Relativistic Matter With Magnetic Fields
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ABSTRACT. Stability of matter with Coulomb forces has been proved for
non-relativistic dynamics, including arbitrarily large magnetic fields,
and for relativistic dynamics without magnetic fields. In both cases
stability requires that the fine structure constant $\alpha$ be not too
large. It was unclear what would happen for {\it both} relativistic
dynamics {\it and} magnetic 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 Dirac operator to define the negative levels leads to
catastrophe for any $\alpha$, but the use of the Dirac operator {\it
with} magnetic field leads to stability. (Appeared in Phys. Rev. Lett.
Vol 79, 1785 (1997)).