Actions for Duality-Symmetric Fields
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The problem of constructing models described by duality-invariant actions has a rather long history. It goes back to time when Poincaré and later on Dirac noticed electric-magnetic duality symmetry of the free Maxwell equations, and, Dirac (1931) assumed the existence of magnetically charged particles (monopoles and dyons) 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. In 1971 Zwanziger constructed such an action. An alternative duality- symmetric Maxwell action was proposed by Deser and Teitelboim in 1976. The two actions, which proved to be dual to each other by Maznytsia et. al. (1998), are not manifestly Lorentz-invariant. This feature turned out to be a general one. Duality and space-time symmetries hardly coexist in one and the same action.