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.

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

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

M3 - Article

AN - SCOPUS:4243945250

VL - 364

SP - 127

EP - 161

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1

ER -