Fields-currents duality in gauge field theories

Abstract:
By using a generalization of the Lie-Poisson brackets for Maxwell field strength tensor and its energy-momentum we construct gauge invariant vector and axial-vector conserved currents for the free Maxwell field. Heaviside-Larmor-Rainich duality transformation of these currents are formally coincide with a duality transformation both electric and magnetic currents.

The construction also applies when external currents are present, for topologically massive gauge field, BF-theory and in the care of spinor and scalar electrodynamics.

The invariance under transformations that involve inversion of charge conjugation (C), parity (P) and time (T) these currents are discussed.