Complex Structures in Electrodynamics

In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure I participates implicitly in the equations and its presence is responsible for the so called duality invariance. We give a new form of the equations showing explicitly the participation of I. In the 4-dimensional formulation the complex structure is extracted directly from the equations, it appears as a linear map Φ in the space of 2-forms on R. It is shown also that Φ may appear through the equivariance properties of the new formulation of the theory. Further we show how this complex structure Φ combines with the Poincaré isomorphism P between the 2-forms and 2-tensors to generate all well known and used in the theory (pseudo)metric constructions on R, and to define the conformal symmetry properties. The equations of Extended Electrodynamics (EED) do not also need these pseudometrics as beforehand necessary structures. A new formulation of the EED equations in terms of a generalized Lie derivative is given.