97-515 E.H. Lieb, H. Siedentop, J.P. Solovej
Stability of Relativistic Matter With Magnetic Fields (18K, LaTeX (ReVTeX format)) Sep 21, 97
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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)).

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