Chiral Symmetry Breaking in the weakly coupled QED in a Magnetic Field

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The catalysis of chiral symmetry breaking in the massless weakly coupled QED in a magnetic field is studied. It is shown that the effect is due to the dimensional reduction $D\to D-2$ in the dynamics of fermion pairing in a magnetic field. The dynamical mass of fermions (energy gap in the fermion spectrum) is determined. The temperature of the symmetry restoration is estimated analytically.
6 pages. REVTeX. The talk given at the International Workshop "Mathematical Physics - today, Priority Technologies -- for tomorrow" (May 12-17, 1997, Kiev, Ukraine) and at the International School of Subnuclear Physics "Highlights: 50 Years Later" (Aug 26 - Sep 4, 1997, Erice-Sicily). The talk is based on a series of papers done in collaboration with V.P.Gusynin and V.A.Miransky

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