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We investigate a theory in which fundamental objects are branes described interms of higher grade coordinates X^{\mu_1 ... \mu_n} encoding both the motionof a brane as a whole, and its volume evolution. We thus formulate a dynamicswhich generalizes the dynamics of the usual branes. Geometrically, coordinatesX^{\mu_1 ... \mu_n} and associated coordinate frame fields {\gamma_{\mu_1 ...\mu_n}} extend the notion of geometry from spacetime to that of an enlargedspace, called Clifford space or C-space. If we start from 4-dimensionalspacetime, then the dimension of C-space is 16. The fact that C-space has morethan four dimensions suggests that it could serve as a realization ofKaluza-Klein idea. The "extra dimensions" are not just the ordinary extradimensions, they are related to the volume degrees of freedom, therefore theyare physical, and need not be compactified. Gauge fields are due to the metricof Clifford space. It turns out that amongst the latter gauge fields there alsoexist higher grade, antisymmetric fields of the Kalb-Ramond type, and theirnon-Abelian generalization. All those fields are naturally coupled to thegeneralized branes, whose dynamics is given by a generalized Howe-Tucker actionin curved C-space.Comment: 41 pages, additional references include

On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb–Ramond Fields