On potentials for several classes of spinor and tensor fields in curved spacetimes |
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Authors: | Reinhard Illge |
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Affiliation: | (1) Sektion Mathematik/Physik der Pädagogischen Hochschule, 5064 Erfurt, German Democratic Republic |
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Abstract: | Already known results with respect to the existence of a vector potential for the Maxwell field tensor and a tensor potential for Weyl's conformal curvature tensor in four-dimensional spacetimes are generalized. It is shown that there exists a spinor potential of type (n–1,1) for any totally symmetric spinor field of rankn. From this theorem we deduce a series of corollaries, for example, that every antisymmetric tensor of second rank admits a linear representation in terms of the first derivatives of two vector fields. Further, some investigations are made on the existence of potentials for arbitrary symmetric spinors of type (n, m). |
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