Not sure whether I understood the intention of your question correctly.

In electrodynamics you usually use a 1-form $A=A_{\mu}dx^{\mu}$ to write down an action
\begin{equation*}
S = \int F \wedge \star F
\end{equation*}
with the 2-form field strength $F=dA$, which the gives the known (vacuum) Maxwell equations.

Scalar fields $\phi$ (such as the Higgs) are described by 0-forms or alternatively by their dual $(d-2)$-forms in $d$ dimensions.

In string theory one finds cousins of the electromagnetic field $A$, but they turn out to be $p$-forms, e.g. in type IIB we have the R-R-fields $C_0, C_2,C_4$,...

psm

This post imported from StackExchange Physics at 2015-10-03 21:47 (UTC), posted by SE-user psm