Magnetic Charge and Dyality Invariance

Abstract: This paper is a critical study of non-standard Maxwellian electrodynamics. It explores two important topics: the inclusion of both magnetic and electric charge to produce what it calls Extended Electrodynamics, and the existence of a symmetry called Dyality Invariance that exchanges electric and magnetic quantities. First, the paper summarizes Extended Electrodynamics, including potentials, gauge transformations, and a new proof of the extended electrodynamic Poynting theorem. A formal Lagrangian derivation of the extended Maxwell equations is also given, but its value in fundamental studies is questioned. The paper then defines Dyality Invariance (form invariance under the so-called Dyality Transformation that exchanges electric and magnetic quantities) and shows it to be a valid symmetry if and only if electrodynamics is given the extended form. The paper suggests that the complete Maxwellian electrodynamics is extended electrodynamics with its dyality invariance. But dyality can be interpreted either actively or passively. Since magnetic charge has not been observed experimentally, the active interpretation is ruled out. But a passive interpretation can be used to avoid writing magnetic source and potential terms explicitly. The paper also refutes the idea that dyality invariance would permit a magnetic charge to be transformed away even if one existed. If nonzero magnetic charge exists, then experimental evidence for its existence cannot be hidden by a dyality transformation.