A generalized gauge principle with gauge fields of various ranks
The standard procedure for making a global phase symmetry local involves the introduction of a rank 1, vector field in the definition of the covariant derivative. It is shown that there exists a generalization of the gauging of a phase symmetry using fields of various ranks in the definition of the covariant derivative. Thus the standard gauge procedure appears as just one (special) possibility for making symmetries local. Some properties and possible uses of these alternative gauge theories will be given.