p-form electrodynamics

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

is the exterior derivative, and a gauge-invariant vector current

with density 1 satisfying the continuity equation where

is the Hodge star operator.

is a gauge-invariant 2-form defined as the exterior derivative

is the exterior derivative, and a gauge-invariant p-vector

with density 1 satisfying the continuity equation where

is a gauge-invariant (p + 1)-form defined as the exterior derivative

This can be derived from the action where M is the spacetime manifold.

The Kalb–Ramond field is an example with p = 2 in string theory; the Ramond–Ramond fields whose charged sources are D-branes are examples for all values of p. In eleven-dimensional supergravity or M-theory, we have a 3-form electrodynamics.

Just as we have non-abelian generalizations of electrodynamics, leading to Yang–Mills theories, we also have nonabelian generalizations of p-form electrodynamics.