Magnetic catalysis of chiral symmetry breaking and the Pauli problem
  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 $\alpha$ = 1/137. 
Y. Jack Ng