GRIBOV PROBLEM FOR GAUGE THEORIES: A PEDAGOGICAL INTRODUCTION

GIAMPIERO ESPOSITO, DIEGO N. PELLICCIA, FRANCESCO ZACCARIA
2004 International Journal of Geometric Methods in Modern Physics (IJGMMP)  
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
more » ... 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.
doi:10.1142/s0219887804000216 fatcat:sncubxxcjbdthowamgddefzxry