# Gribov problem for gauge theories: A Pedagogical introduction

@article{Esposito2004GribovPF, title={Gribov problem for gauge theories: A Pedagogical introduction}, author={Giampiero Esposito and Diego N. Pelliccia and Francesco Zaccaria}, journal={International Journal of Geometric Methods in Modern Physics}, year={2004}, volume={1}, pages={423-441} }

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 nonlinear differential equation, and the various solutions of such a nonlinear 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… Expand

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#### References

SHOWING 1-10 OF 84 REFERENCES

Towards a nonperturbative path integral in gauge theories

- Physics, Mathematics
- 1999

Abstract We propose a modification of the Faddeev–Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit… Expand

Local and renormalizable action from the gribov horizon

- Physics
- 1989

We derive a local, renormalizable action for non-abelian gauge theories, which expresses the restriction of the domain of the functional integral to the interior of the Gribov horizon, and show that… Expand

QCD, gauge-fixing, and the Gribov problem

- Physics
- 2002

Abstract The standard techniques of gauge-fixing, such as covariant gauge fixing, are entirely adequate for the purposes of studies of perturbative QCD. However, they fail in the nonperturbative… Expand

The Gribov ambiguity in gauge theories on the four-torus

- Physics
- 1984

Abstract It is shown that it is impossible to fix the gauge (i.e., there is a Gribov ambiguity) in a non-abelian gauge theory, with any gauge group, defined on the four-torus (which corresponds to a… Expand

Quark confinement and topology of gauge theories

- Physics
- 1977

Abstract The phenomenon of quark confinement is known to be connected with the restoration of apparently broken gauge symmetry. In this paper we focus on a special mechanism which is responsible for… Expand

YANG-MILLS THEORY AS AN ABELIAN THEORY WITHOUT GAUGE FIXING

- Physics
- 1999

Abstract A general procedure to reveal an Abelian structure of Yang-Mills theories by means of a (nonlocal) change of variables, rather than by gauge fixing, in the space of connections is proposed.… Expand

Confinement of Quarks

- Physics
- 1974

A mechanism for total confinement of quarks, similar to that of Schwinger, is defined which requires the existence of Abelian or non-Abelian gauge fields. It is shown how to quantize a gauge field… Expand

Non-perturbative modification of the Faddeev-Popov formula and banishment of the naive vacuum☆

- Physics
- 1982

Abstract It is shown that for a gauge theory with a semisimple Lie group, all gauge orbits intersect a hyperplane in A -space in a convex region Ω which is bounded in every direction. This bounded… Expand

A preliminary study of the Gribov ambiguity in lattice SU(3) Coulomb gauge

- Physics
- 1991

Abstract We report on simulations of pure SU(3) gauge theory on a 10 3 ×20 lattice at β =6.0 in the Coulomb gauge, from which the Gribov ambiguity appears to be maximal, in the sense that the… Expand

Dual superconductor scenario of confinement: A systematic study of Gribov copy effects.

- Physics, Medicine
- Physical review. D, Particles and fields
- 1996

An approximate factorization of the Abelian potential into monopole and photon contributions has been confirmed, the former giving rise to the Abelia string tension. Expand