Gribov ambiguity

In gauge theory, especially in non-abelian gauge theories, global problems at gauge fixing are often encountered. Gauge fixing means choosing a representative from each gauge orbit, that is, choosing a section of a fiber bundle. The space of representatives is a submanifold (of the bundle as a whole) 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. The difficulty arises because the gauge fixing condition is usually specified as a differential equation of some sort, e.g. that a divergence vanish (as in the Landau or Lorenz gauge). The solutions to this equation may end up specifying multiple sections, or perhaps none at all. 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. Still one can show that this problem is not resolved even when reducing the region to the first Gribov region. The only region for which this ambiguity is resolved is the fundamental modular region (FMR).

See also the original paper of Gribov,[1] Heinzl's paper with a quantum-mechanical toy example,[2] and the second slide of Kondo's presentation.[3] A recent discussion of the ambiguity can be found at.[4]

References

  1. ↑ V. N. Gribov. Quantization of non-abelian gauge theories. Nuclear Physics B139 (1978), p.1-19
  2. ↑ T. Heinzl. Hamiltonian Approach to the Gribov Problem. Nuclear Physics B (Proc.Suppl) 54A (1997) 194-197, arXiv:hep-th/9609055,
  3. ↑ http://www.icra.it/MG/mg12/talks/sqg5_kondo.pdf
  4. ↑ A. T. Maas. Gauge bosons at zero and finite temperature. Physics Reports 524 Issue 4 (2013), arXiv:hep-th/11063942


This article is issued from Wikipedia - version of the Saturday, April 30, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.