### Abstract

A detailed analysis is given of chiral-symmetry breaking in the large-flavor (N) limit of quantum electrodynamics in (2+1) dimensions. Analytical and numerical solutions of the homogeneous Dyson-Schwinger equation for the fermion self-energy combined with a computation of the effective potential for the fermion bilinear show that it is energetically preferable for the theory to dynamically generate a mass for fermions. The magnitude of the mass is roughly exponentially suppressed in N from the fundamental dimensionful scale N e2 of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order , so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to . Higher-order 1/N corrections are analyzed and it is shown that the 1/N expansion can be used consistently to demonstrate chiral-symmetry breaking. Open issues and possible improvements of the analysis are given and some avenues for future investigation suggested.

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

Pages (from-to) | 3704-3713 |

Number of pages | 10 |

Journal | Physical Review D |

Volume | 33 |

Issue number | 12 |

DOIs | |

State | Published - 1986 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*33*(12), 3704-3713. https://doi.org/10.1103/PhysRevD.33.3704

**Spontaneous chiral-symmetry breaking in three-dimensional QED.** / Appelquist, Thomas W.; Bowick, Mark John; Karabali, Dimitra; Wijewardhana, L. C R.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 33, no. 12, pp. 3704-3713. https://doi.org/10.1103/PhysRevD.33.3704

}

TY - JOUR

T1 - Spontaneous chiral-symmetry breaking in three-dimensional QED

AU - Appelquist, Thomas W.

AU - Bowick, Mark John

AU - Karabali, Dimitra

AU - Wijewardhana, L. C R

PY - 1986

Y1 - 1986

N2 - A detailed analysis is given of chiral-symmetry breaking in the large-flavor (N) limit of quantum electrodynamics in (2+1) dimensions. Analytical and numerical solutions of the homogeneous Dyson-Schwinger equation for the fermion self-energy combined with a computation of the effective potential for the fermion bilinear show that it is energetically preferable for the theory to dynamically generate a mass for fermions. The magnitude of the mass is roughly exponentially suppressed in N from the fundamental dimensionful scale N e2 of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order , so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to . Higher-order 1/N corrections are analyzed and it is shown that the 1/N expansion can be used consistently to demonstrate chiral-symmetry breaking. Open issues and possible improvements of the analysis are given and some avenues for future investigation suggested.

AB - A detailed analysis is given of chiral-symmetry breaking in the large-flavor (N) limit of quantum electrodynamics in (2+1) dimensions. Analytical and numerical solutions of the homogeneous Dyson-Schwinger equation for the fermion self-energy combined with a computation of the effective potential for the fermion bilinear show that it is energetically preferable for the theory to dynamically generate a mass for fermions. The magnitude of the mass is roughly exponentially suppressed in N from the fundamental dimensionful scale N e2 of the gauge coupling constant, but the scale at which the self-mass begins to damp rapidly appears to be of order , so that there is no spontaneous breaking of an approximate scale invariance that the underlying theory possesses at momentum small compared to . Higher-order 1/N corrections are analyzed and it is shown that the 1/N expansion can be used consistently to demonstrate chiral-symmetry breaking. Open issues and possible improvements of the analysis are given and some avenues for future investigation suggested.

UR - http://www.scopus.com/inward/record.url?scp=26544467802&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=26544467802&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.33.3704

DO - 10.1103/PhysRevD.33.3704

M3 - Article

AN - SCOPUS:26544467802

VL - 33

SP - 3704

EP - 3713

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -