ar X iv : h ep - t h / 98 07 13 3 v 1 1 8 Ju l 1 99 8 HUB EP - 98 / 43 DFPD 98 / TH / 36 hep - th / 9807133

A way of covariantizing duality symmetric actions is described. The presence of self–dual fields or, in more general case, duality–symmetric fields in field–theoretical and string models reflects their duality properties whose extreme importance for understanding a full quantum theory has been appreciated during an impetuous development of the duality field happened during last few years. The knowledge of duality–symmetric effective actions is useful for carrying out more systematic study of the classical and quantum properties of the theory, and in this memorial contribution we would like to demonstrate how fruitful physical ideas and mathematical techniques which Victor Isakovich Ogievetsky and his colleagues have developed helped us to construct a covariant Lagrangian formulation applicable to all known models with duality–symmetric fields in space–time of Lorentz signature. The problem of constructing and studying models described by duality–invariant actions has a rather long history. It goes back to time when Poincare and later on Dirac noticed electric–magnetic duality symmetry of the free Maxwell equations, and, Dirac assumed the existence of magnetically charged particles (monopoles and dyons) [1] admitting the duality symmetry to be also held for the Maxwell equations in the presence of charged sources. To describe monopoles and dyons on an equal footing with electrically charged particles one should have a duality–symmetric form of the Maxwell action. This problem was studied (among others) by Schwinger and 1 Alexander von Humboldt fellow. On leave from Kharkov Institute of Physics and Technology, Kharkov, 310108, Ukraine.