Gribov ambiguity
Encyclopedia
In gauge theory, especially in non-abelian gauge theories, we often encounter global problems when gauge fixing
. Gauge fixing means choosing a representative from each gauge orbit. The space of representatives is a submanifold and represents the gauge fixing condition. Ideally, every gauge orbit will intersect this submanifold once and only once. Unfortunately, this is often impossible globally for non-abelian gauge theories because of topological obstructions and the best that can be done is make this condition true locally. A gauge fixing submanifold may not intersect a gauge orbit at all or it may intersect it more than once. This is called a Gribov ambiguity (named after Vladimir Gribov
).
Gribov ambiguities lead to a nonperturbative failure of the BRST
symmetry, among other things.
A way to resolve the problem of Gribov ambiguity is to restrict the relevant functional integrals to a single Gribov region whose boundary is called a Gribov horizon.
See also the original paper of Gribov, Heinzl's paper with a quantum-mechanical toy example, and the second slide of Kondo's presentation.
Gauge fixing
In the physics of gauge theories, gauge fixing denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field...
. Gauge fixing means choosing a representative from each gauge orbit. The space of representatives is a submanifold and represents the gauge fixing condition. Ideally, every gauge orbit will intersect this submanifold once and only once. Unfortunately, this is often impossible globally for non-abelian gauge theories because of topological obstructions and the best that can be done is make this condition true locally. A gauge fixing submanifold may not intersect a gauge orbit at all or it may intersect it more than once. This is called a Gribov ambiguity (named after Vladimir Gribov
Vladimir Gribov
Vladimir Naumovich Gribov was a prominent Russian theoretical physicist, who worked on high-energy physics, quantum field theory and the Regge theory of the strong interactions.His best known contributions are the pomeron, the DGLAP equations, and the Gribov copies.-Life:Gribov completed his...
).
Gribov ambiguities lead to a nonperturbative failure of the BRST
BRST
BRST may refer to:* BRST formalism and quantization in Yang-Mills theories* Big Red Switch Time , computer jargon for switching your computer off, when all other options for a more elegant shutdown have been exhausted...
symmetry, among other things.
A way to resolve the problem of Gribov ambiguity is to restrict the relevant functional integrals to a single Gribov region whose boundary is called a Gribov horizon.
See also the original paper of Gribov, Heinzl's paper with a quantum-mechanical toy example, and the second slide of Kondo's presentation.