Gribov problem for gauge theories: A Pedagogical introduction

Apr, 2004
24 pages
Published in:
  • Int.J.Geom.Meth.Mod.Phys. 1 (2004) 423-441
e-Print:
Report number:
  • DSF-2004-7,
  • DSF-PREPRINT-2004-7

Citations per year

20072011201520192023012345
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.
Note:
  • 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
  • Gauge theories
  • functional integrals
  • lectures
  • gauge field theory: Yang-Mills
  • quantization
  • path integral
  • transformation: gauge
  • Gribov problem
  • asymptotic behavior
  • general relativity