Jets up to Order a~ ' . 1. 1.! 'fb<~ ~ fc~>i ('J (1.2.5) ~(>r) ~ ~:()(') -r'";eb(d~(!C") +; ~&~.-) 7he requirement of local gauge invariance leads to the unique Lagrangian (1.2.2) Nhich severely restricts the otherwise possible interaction terms between quarks and gluons. This gauge ~~variance is also crucial to make the theory renormalizable (t' Hoeft /1971/l and so yields sensible predictions for physical processes at high energies. Locally gauge invariant theories like QCD are difficult to

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... antize because the fields Aa(x) are gauge quantities and therefore exhibit extra non-physical degrees " of freedom with must be dealt with. The most convenient procedure for quantisation is Fey~' s path integral formalism. For review of this lj:opic see Abers and Lee /1973/, Zinn-Justin /1975/, Bech~r, BOhm and Joos /1981/ and Itzykson and Zuber /1980/. '!be structure of QCD is similar to that of Quantum Electrodyna~~~ics (QED), the only successful field theory we have. In QED, which is an abelian gauge theory, the right hand side of (1.2.1) vanishes and the charged matter fields transform under gauge transformations by simple phase trasformations, i.e. U(1} transforma--10tions. In QCD, being a non-abelian generalization, the quarks transform under the more complicated SU(3) colour group and the vector bosons, the gluons, now carry colour charge too. The Lagrangian (1.2.2) is written in terms of the so-called unrenormalized fields q(x) and A~(x). The calculation of scattering matrix elements or other physical quantities yield finite results only if the theory is renormalized. Th!s means, the infinities of the theory are absorbed into the basic constants of the theory such as coupling constants and masses which are renormalized to their finite physical values. Therefore these coupling constants and masses must be given and cannot be calculated in this theory. The technique for renormalizing perturbative QCD is well known from QED. The fields are multiplicatively renormalized, i.e. one defines renormalized fields q and A a