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Gribov Problem for Gauge Theories: a Pedagogical Introduction

Giampiero Esposito·Diego N. Pelliccia·Francesco Zaccaria
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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.

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Giampiero Esposito, Diego N. Pelliccia, Francesco Zaccaria. 2004-05-03. Gribov Problem for Gauge Theories: a Pedagogical Introduction. https://doi.org/10.1142/s0219887804000216

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