### Abstract

A minimal Landau gauge is defined by choosing the gauge which minimizes the action S_{L}(U) ≡ -Σ Re tr U, where the sum extends over all links of the lattice, and a minimal Coulomb gauge is defined analogously. The positivity of the second variation of this action at a minimum determines the lattice Gribov region. It is shown that if an external "magnetic" field H is coupled to the color spins then, in the infinite-volume limit, the color magnetization M(H) vanishes identically for all H. Consequently all gluon correlation functions vanish at zero-momentum. This implies a maximal violation of reflection positivity for gluons in a minimal Landau gauge. A confinement mechanism is hypothesized whereby color-singlet gauge-invariant states are stabilized by reflection positivity which gives them a real mass, whereas color non-singlet objects are unstable because they are not gauge invariant and consequently develop a complex mass, which is observable, in principle, in jet events.

Original language | English (US) |
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Pages (from-to) | 127-161 |

Number of pages | 35 |

Journal | Nuclear Physics, Section B |

Volume | 364 |

Issue number | 1 |

DOIs | |

State | Published - Oct 14 1991 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*364*(1), 127-161. https://doi.org/10.1016/0550-3213(91)90581-H

**Vanishing of zero-momentum lattice gluon propagator and color confinement.** / Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 364, no. 1, pp. 127-161. https://doi.org/10.1016/0550-3213(91)90581-H

}

TY - JOUR

T1 - Vanishing of zero-momentum lattice gluon propagator and color confinement

AU - Zwanziger, Daniel

PY - 1991/10/14

Y1 - 1991/10/14

N2 - A minimal Landau gauge is defined by choosing the gauge which minimizes the action SL(U) ≡ -Σ Re tr U, where the sum extends over all links of the lattice, and a minimal Coulomb gauge is defined analogously. The positivity of the second variation of this action at a minimum determines the lattice Gribov region. It is shown that if an external "magnetic" field H is coupled to the color spins then, in the infinite-volume limit, the color magnetization M(H) vanishes identically for all H. Consequently all gluon correlation functions vanish at zero-momentum. This implies a maximal violation of reflection positivity for gluons in a minimal Landau gauge. A confinement mechanism is hypothesized whereby color-singlet gauge-invariant states are stabilized by reflection positivity which gives them a real mass, whereas color non-singlet objects are unstable because they are not gauge invariant and consequently develop a complex mass, which is observable, in principle, in jet events.

AB - A minimal Landau gauge is defined by choosing the gauge which minimizes the action SL(U) ≡ -Σ Re tr U, where the sum extends over all links of the lattice, and a minimal Coulomb gauge is defined analogously. The positivity of the second variation of this action at a minimum determines the lattice Gribov region. It is shown that if an external "magnetic" field H is coupled to the color spins then, in the infinite-volume limit, the color magnetization M(H) vanishes identically for all H. Consequently all gluon correlation functions vanish at zero-momentum. This implies a maximal violation of reflection positivity for gluons in a minimal Landau gauge. A confinement mechanism is hypothesized whereby color-singlet gauge-invariant states are stabilized by reflection positivity which gives them a real mass, whereas color non-singlet objects are unstable because they are not gauge invariant and consequently develop a complex mass, which is observable, in principle, in jet events.

UR - http://www.scopus.com/inward/record.url?scp=4243945250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243945250&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(91)90581-H

DO - 10.1016/0550-3213(91)90581-H

M3 - Article

VL - 364

SP - 127

EP - 161

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1

ER -