Abstract
A new and concise proof ofexistence - emphasizing the very naturaland simple structure - is given for theLanczos spinor potential LABCA' of anarbitrary symmetric spinor WABCDdefined by WABCD = 2∇(AA'LBCD)A'; this proof is easily translated into tensorsin such a way that it is valid in four-dimensional spaces of any signature.In particular, this means that the Weyl spinor ΨABCD has Lanczospotentials in all spacetimes, and furthermore that the Weyl tensor hasLanczos potentials on all four-dimensional spaces, irrespective ofsignature. In addition, two superpotentials for WABCD are identified:the first TABCD ( = T(ABC)D) isgiven by LABCA' = ∇A'DTABCD, while the secondHABA'B' ( = H(AB)(A'B')) (which isrestricted to Einstein spacetimes) is givenbyLABCA' = ∇(AB'HBC)A'B'. The superpotential TABCD is used to describe the gaugefreedom in the Lanczos potential.
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