Strings and p-branes with or without spin degrees of freedom and q-form fields

A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools come from the well-known de Rham-Kodaira decomposing theorem on the harmonic integral. We have a field-theoretic action suitable for strings and $p$-branes with or without spin degrees of freedom. In a completely-kinematical way is derived the generalized Maxwell theory with a magnetic monopole over a curved space-time, where we have a new type of gauge transformations.