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Alternative gauge procedure with fields of various ranks
Making a global phase symmetry local usually involves the introduction of a rank 1, vector field in the definition of the covariant derivative. In this paper we show how a symmetry can be gauged using fields of various ranks in the definition of the covariant derivative. Some of these higher rank gauge theories share similarities with general relativity in that the covariant derivative has terms which are derivatives of some more fundamental quantity. Most of the Lagrangians that we find under these higher rank gauge theories lead to nonrenormalizable quantum theories which is also similar to general relativity.