Bulk quantization of gauge theories: Confined and higgs phases

Laurent Baulieu, Daniel Zwanziger

    Research output: Contribution to journalArticlepeer-review


    We deepen the understanding of the quantization of the Yang-Mills field by showing that the concept of gauge fixing in 4 dimensions is replaced in the 5-dimensional formulation by a procedure that amounts to an A-dependent gauge transformation. The 5-dimensional formulation implements the restriction of the physical 4-dimensional gluon field to the Gribov region, while being a local description that is under control of BRST symmetries both of topological and gauge type. The ghosts decouple so the euclidean probability density is everywhere positive, in contradistinction to the Faddeev-Popov method for which the determinant changes sign outside the Gribov region. We include in our discussion the coupling of the gauge theory to a Higgs field, including the case of spontaneously symmetry breaking. We introduce a minimizing functional on the gauge orbit that could be of interest for numerical gauge fixing in the simulations of spontaneously broken lattice gauge theories. Other new results are displayed, such as the identification of the Schwinger-Dyson equation of the five dimensional formulation in the (singular) Landau gauge with that of the ordinary Faddeev-Popov formulation, order by order in perturbation theory.

    Original languageEnglish (US)
    Pages (from-to)1-32
    Number of pages32
    JournalJournal of High Energy Physics
    Issue number8
    StatePublished - 2001


    • BRST Quantization
    • Non-perturbative Effects
    • QCD
    • Renormalization Regularization and Renormalons

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics


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