Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor

Details Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor Existence of Lanczos potentials and superpotentials for the Weyl spinor/tensor

Jun 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001cqgra..18.2297a&link_type=abstract

Classical and Quantum Gravity, Volume 18, Issue 12, pp. 2297-2304 (2001).

Physics

3

Scientific paper

A new and concise proof of existence - emphasizing the very natural and simple structure - is given for the Lanczos spinor potential LABCA' of an arbitrary symmetric spinor WABCD defined by WABCD = 2∇(AA'LBCD)A' this proof is easily translated into tensors in such a way that it is valid in four-dimensional spaces of any signature. In particular, this means that the Weyl spinor ΨABCD has Lanczos potentials in all spacetimes, and furthermore that the Weyl tensor has Lanczos potentials on all four-dimensional spaces, irrespective of signature. In addition, two superpotentials for WABCD are identified: the first TABCD ( = T(ABC)D) is given by LABCA' = ∇A'DTABCD, while the second HABA'B' ( = H(AB)(A'B')) (which is restricted to Einstein spacetimes) is given by LABCA' = ∇(AB'HBC)A'B'. The superpotential TABCD is used to describe the gauge freedom in the Lanczos potential.

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