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**1 - 1**of**1**### Explicit Actions for Electromagnetism with Two Gauge Fields with Only one Electric and one Magnetic Physical Fields

, 2006

"... We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physi ..."

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We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physical fields and are invariant under the discrete symmetries P and T. We conclude that neither the Lagrangian, nor the Hamiltonian, are invariant under the electromagnetic duality rotations. This agrees with the weak-strong coupling mixing characteristic of the duality due to the Dirac quantization condition providing a natural way to differentiate dual theories related by the duality rotations (the energy is not invariant). Also the standard electromagnetic duality rotations considered in this work violate both P and T by inducing Hopf terms (theta terms) for each sector and a mixed Maxwell term. The canonical structure of the theory is briefly addressed and the magnetic gauge sector is interpreted as a ghost sector.