Nuclear Physics B186 (1981) 165-186 © North-Holland Publishing Company eVITANOVlc COl ft- c 1-l M ('1' j GAUGE INVARIANCE STRUCTURE OF QUANTUM CHROMODYNAMICS Predrag CVITANOVIC Nordita, Blegdamsvej 17, DK-2100 Copenhagen ((1, Denmark P.G. LAUWERS and P.N. SCHARBACH' The Niels Bohr Institute, Copenhagen /21, Denmark Received 22 December 1980 (Final version received 19 February 1981) Perturbative QeD may be subdivided into separately gauge-invariant sectors according to the projection of non-abelian color weights onto linearly independent basis elements. We exploit the general Lie group structure of the theory to give an algorithm for finding these gauge-invariant sets and present several examples of its use. The planar sector and the systematks of the non-planar corrections are defined for any gauge theory. Our gauge set classification has implications for QCD bound states, finite order perturbative QeD calculations, the study of QCD infrared singularities and for the question of convergence of the perturbation series. 1. Introduction For lhe purposes of this paper we shall consider QCD as a non-abelian gauge theory of quarks and gluons defined by the perturbation expansion. The physics of the theory so defined may involve sums of infinite numbers of Feynman diagrams, but is perturbative in the sense that all contributions follow from the basic vertices of the theory, and not from non-perturbative phenomena such as instantons. At presenl we are unable to carry out the momentum integrations for arbitrarily complicated diagrams. On the other hand, one should investigate whether it is possible to organize this infinity of QCD diagrams before we tackle the problem of actually evaluating and summing them. At first glance it would seem that there is not much that one can do. Each diagram is gauge dependent and physicallymeaningless by itself; the textbook proofs ofgauge invariance of physical quantities assume the inclusion of all Feynman diagrams contributing in a given order. However, for quantum electrodynamics this is not the whole story; in actual perturbative calculations one soon discovers that the full set of diagrams may be subdivided into "gauge sets"; subsets which are individually gauge invariant [1-3]. This decomposition can be very useful in practice, as it is often convenient to perform different parts of the calculation in different gauges [3]. It is 1 Present address: Rutherford Laboratory, Chilton, Didcot, Oxon., England. 165