Constituent quarks from QCD by Martin Lavelle; David MacMullan

By Martin Lavelle; David MacMullan

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S 8 and 9. The results of this subsection show the great sensitivity of the theory to the type of dressing employed. In Sect. 9 we will study how to boost a charge and how the dressing must then be altered. We will in particular see that Coulomb gauge does not then remove the dressing, which indicates why it is not possible to carry out a non-static mass shell renormalisation scheme for static charges. We conclude this subsection by repeating that no problems were encountered in renormalising the physical fields as long as the correct renormalisation scheme was used.

19) does not uniquely fix h. 14) cannot be constructed. This is not an artifact of the Coulomb gauge condition and, as shown by Singer[49] , occurs for all gauge fixing conditions defined on A. This has become known as the Gribov ambiguity. This existence of this ambiguity is central to our account of confinement in QCD, hence it is helpful to briefly explain how it arises. We have identified the group of all local gauge transformations G with the mappings from space time R4 to the structure group SU (3) which tend to the constant 1 at spatial infinity.

This shows that the leading OPE correction is, as we had hoped, gauge-invariant. The remainder may be found by evaluating each of the diagrams in Feynman gauge. 22) which result has been previously obtained[79] as the leading OPE correction to the Coulomb gauge quark propagator9 . In the instantaneous approximation this is just the standard Landau gauge result. 22). We now have to interpret this result. , for large p2 . 23) is that OPE effects from the quark condensate introduce gauge-invariant, non-perturbative corrections in the dressed quark propagator which have a power-like fall off and introduce a running mass scale.

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