### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 249-290 |

Number of pages | 42 |

Journal | Nuclear Physics B |

Volume | 462 |

Issue number | 2-3 |

State | Published - Mar 11 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*462*(2-3), 249-290.

**Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field.** / Gusynin, V. P.; Miransky, V. A.; Shovkovy, Igor.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 462, no. 2-3, pp. 249-290.

}

TY - JOUR

T1 - Dimensional reduction and catalysis of dynamical symmetry breaking by a magnetic field

AU - Gusynin, V. P.

AU - Miransky, V. A.

AU - Shovkovy, Igor

PY - 1996/3/11

Y1 - 1996/3/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030579691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030579691&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030579691

VL - 462

SP - 249

EP - 290

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2-3

ER -