Several features of the static quark-ant~quark potent~al ~n quantum cl~romodynamics are studled. It 1s shown, first of all, that the potentlal between fixed color sources exlsts as the ~nfin~te-mass l~mlt of the interdctlon between a heavy quark and ant~quark The phenomenological consequences of thls result are summarized The potentlal 1s then examlned as an expansion In the strong-coupl~ng constant a, using the Wllson loop Integral Infrared properties are elucidated and the power-series expansion In a, 1s s h o~n to break down The quantum color correlations of the qudrk sources w~t h the gluon field Induce singulafities which can only be removed by selectlve resummation The resulting expresslon for the potent~al 1s nonanalytlc in a, at a, = 0

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We examine the problems of calculating the leading relativistic corrections to heavyquarkonium decays [relative O(v2)] within the context of QCD. The incorporation of constituent motion in a consistent manner poses nontrivial problems associated with gauge invariance and multiple counting with higher-order contributions in the coupling constant. Although we were unable to resolve these questions in a completely satisfactory manner, we present an improved static limit where the kinematic relativistic corrections are included through binding effects. Our results are gauge invariant and in qualitative agreement with the relative size of relativistic corrections suggested in the analysis of the branching ratio of r(3g)/r(~T) in the $ / J and ' Y systems in QCD.

We calculate the leading quantum and semi-classical corrections to the Newtonian potential energy of two widely separated static masses. In this largedistance, static limit, the quantum behaviour of the sources does not contribute to the quantum corrections of the potential. These arise exclusively from the propagation of massless degrees of freedom. Our one-loop result is based on Modanese's formulation and is in disagreement with Donoghue's recent calculation. Also, we compare and contrast the structural similarities of our approach to scattering at ultra-high energy and large impact parameter.We connect our approach to results from string perturbation theory.

Recent observations on ambiguities of the Coulomb gauge in Yang-Mills theories are clarified. We point out that discontinuities of the transverse potentials are necessary in order to accommodate arbitrary Pontryagin index. A general argument is given along formal lines, and a numerical example is presented for an O(3)-symmetric gauge-field configuration. The one-pseudoparticle solution is transformed into the Coulomb gauge, and the mechanism for the emergence of an angle characterizing the vacuum is indicated.

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