Abstract
Let us consider the set of fields that we have postulated for QCD: three q i (x) for each flavor of quark, and eight B a (x).
Puisque ces mystères nous depassent, feignons de les avoir organisés
J. Cocteau
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Again, the analogy of Guva with the electromagnetic field strength tensor, fuv = 0uAv — 0v Au is apparent.
Peculiar gauges with ghosts may also be constructed for Abelian theories.
A potential “tadpole” contribution (Figure 2.3.1e) has been omitted because in dimensional regulariz-ation, fadDk(k 2 + i0) - 1 - o Cf. Section 3.1.
It is convenient at times, although not necessary, to think of th w as mutually adjoint. The formal deduction of (2.3.8) to all orders will be given in Section 2.5.
Moreover, it presents extra complications. The formulation of QCD in a Coulomb gauge may be found in Christ and Lee (1980).
Axial gauges are discussed in Kummer (1975) and work quoted there. See, for example, Tomboulis (1973) and references therein.
We follow the discussion of de Rafael (1977,1979).
Hence e 2 = 0, ECO = — we, Eq = — qe, eB = Be etc. Remember also that the ww are fermions so we may take wbwc = — wcwwb
In the quantum version, we understand that products are replaced by Wick ordered products. For a discussion of the arbitrariness in the definition of the energy momentum tensor, cf., Callan, Coleman, and Jackiw (1970) and Collins, Duncan, and Joglekar (1977). CI is not unique, and, as a matter of fact, from (2.8.1) above, we do not obtain a gauge-invariant tensor. The expression (2.8.2) is obtained by replacing derivatives with covariant derivatives. Alter-natively, we may reformulate (2.8.1) by performing gauge transformations simultaneously to the translation xu—+ xg + ru For example, writing BB
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© 1993 Springer-Verlag Berlin Heidelberg
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Ynduráin, F.J. (1993). QCD as a Field Theory. In: The Theory of Quark and Gluon Interactions. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02940-4_2
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