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Subject of our investigations is QCD formulated in terms of physical degreesof freedom. Starting from the Faddeev-Popov procedure, the canonicalformulation of QCD is derived for static gauges. Particular emphasis is put onobstructions occurring when implementing gauge conditions and on theconcomitant emergence of compact variables and singular fields. A detailedanalysis of non-perturbative dynamics associated with such exceptional fieldconfigurations within Coulomb- and axial gauge is described. We presentevidence that compact variables generate confinement-like phenomena in bothgauges and point out the deficiencies in achieving a satisfactorynon-perturbative treatment concerning all variables. Gauge fixed formulationsare shown to constitute also a useful framework for phenomenological studies.Phenomenological insights into the dynamics of Polyakov loops and monopoles inconfined and deconfined phases are presented within axial gauge QCDComment: 40 pages, 4 figures, Contribution to the Festschrift in honor of  Boris Ioffe, edited by M. Shifma

COMPACT VARIABLES AND SINGULAR FIELDS IN QCD