Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field

V. P. Gusynin, V. A. Miransky, I. A. Shovkovy

Research output: Contribution to journalArticlepeer-review

473 Scopus citations


It is shown that a constant magnetic field in 3+1 and 2+1 dimensions is a strong catalyst of dynamical chiral symmetry breaking, leading to the generation of a fermion dynamical mass even at the weakest attractive interaction between fermions. The essence of this effect is the dimensional reduction D → D - 2 in the dynamics of fermion pairing in a magnetic field. The effect is illustrated in the Nambu-Jona-Lasinio (NJL) model and QED. In the NJL model in a magnetic field, the low-energy effective action and the spectrum of long-wavelength collective excitations are derived. In QED (in ladder and improved ladder approximations) the dynamical mass of fermions (energy gap in the fermion spectrum) is determined. Possible applications of this effect and its extension to inhomogeneous field configurations are discussed.

Original languageEnglish (US)
Pages (from-to)249-290
Number of pages42
JournalNuclear Physics B
Issue number2-3
StatePublished - Mar 11 1996
Externally publishedYes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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