2 Covariance of Gauge Invariant Operators Un -

The cohomology of the BRS operator corresponding to a group of rigid symmetries is studied in a space of local field functionals subjected to a condition of gauge invariance. We propose a procedure based on a filtration operator counting the degree in the infinitesimal parameters of the rigid symmetry transformations. An application to Witten’s topological Yang-Mills theory is given. PACS codes: 11.15.-q (gauge field theories), 03.65.Fd (algebraic methods), 03.70 (theory of quantized fields) Supported in part by the Swiss National Science Foundation and by OFES contract 93.0083 and Human Capital and Mobility, EC contract ERBCHRXCT920069 Laboratoire de Physique Théorique ENSLAPP, URA 14-36 du CNRS, associee à l’ENS de Lyon, à l’université de Savoie et au LAPP, groupe de Lyon, ENS Lyon, Allée d’Italie 46, F-69364 Lyon, France Département de Physique Théorique, Université de Genève, quai E. Ansermet 24, CH-1211 Genève 4, Switzerland On leave of absence from Università degli Studi di Genova, Dipartimento di Fisica, Italy Instituto da F́ısica, Universidade Católica de Petrópolis, 25610-130 Petrópolis, RJ, Brazil and Centro Brasileiro de Pesquisas F́ısicas (CBPF), Rua Xavier Sigaud 150, 22290-180 Urca, RJ, Brazil On leave of absence from Département de Physique Théorique, Université de Genève, Switzerland. Supported in part by the Brazilian National Research Council (CNPq)