On potentials for several classes of spinor and tensor fields in curved spacetimes.

Details On potentials for several classes of spinor and tensor fields in curved spacetimes. On potentials for several classes of spinor and tensor fields in curved spacetimes.

Jun 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988gregr..20..551i&link_type=abstract

General Relativity and Gravitation, Volume 20, Issue 6, pp.551-564

Physics

33

Gravitation Theory

Scientific paper

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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