Summary
General action of fields on the curved space-time is proposed through de Rham-Kodaira’s decomposing theorem of differential forms. This action describes an extended object such as a string and membrane with spins.Kinematically deduced are the Maxwell equations with a monopole in ann-dimensional curved space-time.
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There is an instance wheref(x) is given by the δ-boundary of some 1-form. This is treated in the same way (and in the more trivial way) as in case 2.
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Miyazaki, T. De Rham-Kodaira’s theorem and general action withq-forms. Nuov Cim B 110, 403–408 (1995). https://doi.org/10.1007/BF02741448
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DOI: https://doi.org/10.1007/BF02741448