Vanishing of zero-momentum lattice gluon propagator and color confinement

Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)127-161
    Number of pages35
    JournalNuclear Physics, Section B
    Volume364
    Issue number1
    DOIs
    StatePublished - Oct 14 1991

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

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