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.
International Journal of Geometric Methods in Modern Physics
- Pub Date:
- August 2004
- High Energy Physics - Theory
- 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