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By Martin Lavelle; David MacMullan

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H The final topic we want to address in this section is the obstruction to extending this construction of the dressing beyond perturbation theory. From our discussion we have seen that a dressing for the quark is equivalent to finding a gauge fixing. So the existence of a dressing is inextricably connected with the existence of a gauge fixing condition. Now Gribov[52] has explicitly demonstrated that the Coulomb gauge in Yang-Mills theory does not exist outside of perturbation theory. 19) does not uniquely fix h.

We need to find h ∈ SU (3) such that under local gauge transformations we have h → hU = U −1 h . 1) Then a physical quark can be identified with the BRST invariant combination ψphys = h−1 ψ . 12) we see that our expression for the static quark corresponds to taking ψcg = −vc + O(g 3 ) and, to this order, h−1 c ψ with hc = e vc = g ∂i A i ∂j ∂i A i ∂i A i 1 ∂j − 12 g 2 2 Aj , 2 − 12 g 2 2 Aj , 2 2 ∇ ∇ ∇ ∇ ∇ . 2) for Lie-algebra valued fields and hence the commutators are Lie-algebra commutators.

2. We work in a general Lorentz gauge. It is natural to divide the calculation into two steps: firstly we calculate the terms which depend upon the gauge parameter in the diagrams and, after we have satisfied ourselves that their sum vanishes, we calculate the gauge-independent OPE correction. 2a, c and d) in the mass. ¯ /)n ψ , can be related via the equation of motion Higher order condensates, of the form ψ(∂ ¯ +O(g) and should be introduced in order to investigate the gauge independence to mn ψψ of these corrections.

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