Magnetic catalysis of chiral symmetry breaking and the Pauli problem

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The non-perturbative Schwinger-Dyson equation is used to show that chiral symmetry is dynamically broken in QED at weak gauge couplings when an external uniform magnetic field is present. A complete analysis of this phenomenon may shed light on the Pauli problem, namely, why $α$ = 1/137.
7 pages, Tex; to appear in the Proceedings of the Conference on Quantum Aspects of Beam Physics, held at Monterey, California in January 1998

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