P-form electrodynamics

In theoretical physics, p-form electrodynamics is a generalization of Maxwell's theory of electromagnetism.

We have a one-form ${\displaystyle \mathbf {A} }$, a gauge symmetry

where ${\displaystyle \alpha }$ is any arbitrary fixed 0-form and ${\displaystyle d}$ is the exterior derivative, and a gauge-invariant vector current ${\displaystyle \mathbf {J} }$ with density 1 satisfying the continuity equation

...
Wikipedia