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

TL;DR

This paper introduces a general field-theoretic action for q-form fields on arbitrary manifolds, applicable to strings and p-branes with or without spin, incorporating generalized Maxwell theory with magnetic monopoles.

Contribution

It develops a unified action framework for differential form fields relevant to strings and p-branes, utilizing de Rham-Kodaira decomposition and introducing new gauge transformations.

Findings

Formulation of a general action for q-form fields on arbitrary manifolds.

Derivation of a generalized Maxwell theory with magnetic monopoles in curved spacetime.

Introduction of new gauge transformation types for these fields.

Abstract

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.