Abstract: We present a covariant Lagrangian formulation for p-form fields in Minkowski spaces of arbitrary dimensions that treat electric and magnetic degrees of freedom on equal footing.
This formulation allows the inclusion of arbitrary abelian self-interactions. In d=4k+2, we cover all abelian self-interactions of a chiral (self-dual) 2k-form, the most interesting example being d=6 (we also comment on d=2 and 10), where the general abelian self-interactions are parametrized by a function of one variable. For d=4k, we cover all abelian self-interactions of (2k-1)-forms, including those with SO(2) duality symmetry. For d=4, we give a simple democratic actionfor arbitrary non-linear electrodynamics involving an arbitrary function of two variables and its duality symmetric subclass manifesting SO(2) symmetry, parametrized by a function of one variable.
This construction, in particular, covers all interesting examples in the literature.