Nonperturbative Landau gauge and infrared critical exponents in QCD

Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in the Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators D(k) and G(k) in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by D (k) ∼ 1/(k2)1+aD and G(k) ∼ 1/(k2)1+aG, are obtained in space-time dimensions d = 2, 3, 4. Two possible solutions are obtained with the values, in d = 4 dimensions, aG = 1, aD = -2, or aG = (93- √1201)/98≈0.595353, aD = -2aG.

    Original languageEnglish (US)
    Article number094039
    Pages (from-to)940391-9403913
    Number of pages8463523
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume65
    Issue number9 B
    StatePublished - May 1 2002

    Fingerprint

    Critical Exponents
    horizon
    Horizon
    Gauge
    Infrared
    quantum chromodynamics
    exponents
    Quantization
    Functional Integral
    ghosts
    Propagator
    ambiguity
    Anomalous
    Resolve
    cut-off
    Limiting
    Space-time
    formulations
    propagation
    Formulation

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Nuclear and High Energy Physics

    Cite this

    Nonperturbative Landau gauge and infrared critical exponents in QCD. / Zwanziger, Daniel.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 65, No. 9 B, 094039, 01.05.2002, p. 940391-9403913.

    Research output: Contribution to journalArticle

    @article{05b21021e5844b51b7f54d10d26012af,
    title = "Nonperturbative Landau gauge and infrared critical exponents in QCD",
    abstract = "We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in the Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators D(k) and G(k) in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by D (k) ∼ 1/(k2)1+aD and G(k) ∼ 1/(k2)1+aG, are obtained in space-time dimensions d = 2, 3, 4. Two possible solutions are obtained with the values, in d = 4 dimensions, aG = 1, aD = -2, or aG = (93- √1201)/98≈0.595353, aD = -2aG.",
    author = "Daniel Zwanziger",
    year = "2002",
    month = "5",
    day = "1",
    language = "English (US)",
    volume = "65",
    pages = "940391--9403913",
    journal = "Physical review D: Particles and fields",
    issn = "1550-7998",
    publisher = "American Institute of Physics",
    number = "9 B",

    }

    TY - JOUR

    T1 - Nonperturbative Landau gauge and infrared critical exponents in QCD

    AU - Zwanziger, Daniel

    PY - 2002/5/1

    Y1 - 2002/5/1

    N2 - We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in the Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators D(k) and G(k) in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by D (k) ∼ 1/(k2)1+aD and G(k) ∼ 1/(k2)1+aG, are obtained in space-time dimensions d = 2, 3, 4. Two possible solutions are obtained with the values, in d = 4 dimensions, aG = 1, aD = -2, or aG = (93- √1201)/98≈0.595353, aD = -2aG.

    AB - We discuss Faddeev-Popov quantization at the nonperturbative level and show that Gribov's prescription of cutting off the functional integral at the Gribov horizon does not change the Schwinger-Dyson equations, but rather resolves an ambiguity in the solution of these equations. We note that Gribov's prescription is not exact, and we therefore turn to the method of stochastic quantization in its time-independent formulation, and recall the proof that it is correct at the nonperturbative level. The nonperturbative Landau gauge is derived as a limiting case, and it is found that it yields the Faddeev-Popov method in the Landau gauge with a cutoff at the Gribov horizon, plus a novel term that corrects for overcounting of Gribov copies inside the Gribov horizon. Nonperturbative but truncated coupled Schwinger-Dyson equations for the gluon and ghost propagators D(k) and G(k) in the Landau gauge are solved asymptotically in the infrared region. The infrared critical exponents or anomalous dimensions, defined by D (k) ∼ 1/(k2)1+aD and G(k) ∼ 1/(k2)1+aG, are obtained in space-time dimensions d = 2, 3, 4. Two possible solutions are obtained with the values, in d = 4 dimensions, aG = 1, aD = -2, or aG = (93- √1201)/98≈0.595353, aD = -2aG.

    UR - http://www.scopus.com/inward/record.url?scp=0036577365&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0036577365&partnerID=8YFLogxK

    M3 - Article

    VL - 65

    SP - 940391

    EP - 9403913

    JO - Physical review D: Particles and fields

    JF - Physical review D: Particles and fields

    SN - 1550-7998

    IS - 9 B

    M1 - 094039

    ER -