Monopoles and Quark Confinement: Introduction and Overview

Abstract

We (try to) pedagogically explain how monopoles arise in QCD, why maximal Abelian(MA) gauge is ``special'' for monopole study, the Abelian projection in MA gauge, its resultant degrees of freedom(photons, monopoles and charged matter fields), and the QCD-equivalent action in terms of these degrees of freedom. Then we turn to more recent developments in the subject: Abelian dominance, large $N$ behavior of Abelian projected QCD, mass of the charged matter fields, notion of an effective photon-monopole action obtained by integrating out the charged matter fields, and problems encountered in the recent evaluation of this effective action using the microcanonical demon method on the lattice.