Not sure whether I understood the intention of your question correctly.
In electrodynamics you usually use a 1-form A=Aμdxμ to write down an action
S=∫F∧⋆F
with the 2-form field strength
F=dA, which the gives the known (vacuum) Maxwell equations.
Scalar fields ϕ (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 C0,C2,C4,...
psm
This post imported from StackExchange Physics at 2015-10-03 21:47 (UTC), posted by SE-user psm