TY - JOUR
T1 - Vanishing of zero-momentum lattice gluon propagator and color confinement
AU - Zwanziger, Daniel
N1 - Funding Information:
*Research supported in part by the National Science Foundation under grant no. PHY 87-15995. *For the current status of jet physics see the first of ref. [2] and for theoretical calculations see the second of ref. [2].
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
SN - 0550-3213
VL - 364
SP - 127
EP - 161
JO - Nuclear Physics, Section B
JF - Nuclear Physics, Section B
IS - 1
ER -