Gribov Problem for Gauge Theories: a Pedagogical Introduction

Abstract

The functional-integral quantization of non-Abelian gauge theories is affected by the Gribov problem at non-perturbative level: the requirement of preserving the supplementary conditions under gauge transformations leads to a non-linear differential equation, and the various solutions of such a non-linear equation represent different gauge configurations known as Gribov copies. Their occurrence (lack of global cross-sections from the point of view of differential geometry) is called Gribov ambiguity, and is here presented within the framework of a global approach to quantum field theory. We first give a simple (standard) example for the SU(2) group and spherically symmetric potentials, then we discuss this phenomenon in general relativity, and recent developments, including lattice calculations.

24 pages, Revtex 4. In the revised version, a statement has been amended on page 11, and References 14, 16 and 27 have been improved

References in corpus (2)

• Non-perturbative Faddeev-Popov formula and infrared limit of QCD
• Lattice calculation of gluon screening masses

Cited by in corpus (16)

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• Ghost anomalous dimension in asymptotically safe quantum gravity
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• Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
• Faddeev-Popov ghosts in quantum gravity beyond perturbation theory
• Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies
• Gribov pendulum in the Coulomb gauge on curved spaces
• Gravitationally induced zero modes of the Faddeev-Popov operator in the Coulomb gauge for Abelian gauge theories
• Gribov ambiguity in asymptotically AdS three-dimensional gravity
• The Fröhlich-Morchio-Strocchi mechanism and quantum gravity
• Size of the Gribov region in curved spacetime
• The Gribov problem in presence of background field for $SU(2)$ Yang-Mills theory
• Abelian gauge theories on compact manifolds and the Gribov ambiguity
• Hidden Gauge Symmetry in Holomorphic Models
• On infrared problems of effective Lagrangians of massive spin 2 fields coupled to gauge fields
• Quantum fields in the non-perturbative regime - Yang-Mills theory and gravity