Nuclear PhysmsB246 (1984) 246-252 © North-Holland PubhsbangCompany RENORMALIZATION OF GAUGE THEORIES: NON-LINEAR GAUGES J ZINN-JUSTIN Serotce de PhyszqueThbortque, CEN-SA CLA Y, 91191 Gtf sur Yvette, Cedex, France Recewed 28 May 1984 The renormahzed actton for gauge theories quantazed w~th non-hnear gauge condxtaons xs written down m ~ts most general form A natural mterpretatton of the well-known quarttc ghost term generated by renormalmattonts gwen m terms of a generahzed Faddeev-Popovdetemunant 1. Introduction This short note presents mainly a (hopefully) pedagogical exercise which outhnes some propertms of the renormahzation of gauge theories m non-linear gauges, implicit in many early works, but may not be sufficiently publicized or written down m standard text books [1]*. In particular a natural interpretation of the quartic ghost term [2] wluch appears in the renormalization of these gauges will be provided. A further motivation for having these properties explicitly written down is that they are useful in the discussion of the renormalization of some dynamical statistmal models [3]. The notation and conventions which I shall use throughout this artmle are those of my Bonn lectures 1974 [4]. In particular I shall use the supercompact notations in which unique indtces stand for space, Lorentz group index, and group radices. Summatmn over repeated indices will always be meant. 2. Renormalization in non-linear gauge I shall call A, the set of all fields of the theory (for simplicity I shall consider only boson fields), the index t standing for all indices and space-time arguments. The gauge invariant acUon will be E(A), and the gauge fixing term Fo(A). The ghosts fields will be denoted by C. and Ca. An infinitesimal gauge transformation of parameters ~0o will be written as 8A,= D~( A)o:,,. (1) * For early references see the first 6 references m [1] The rest probably gdvesthe most soplusttcated &scussxonof renormahzationproblems 246