Problem of Rainich for Two-Component Spinors

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Abstract
Some general relations for two‐component spinors in general relativity are derived in an attempt to solve the problem of Rainich for this case. A set of algebraic equations allows us in principle to express the current vector in terms of the energy‐momentum tensor, and thus in terms of the Einstein tensor, but we have not succeeded in solving these equations except in a special frame of reference. Weyl's equations are expressed in terms of the current vector, its derivatives, and the energy‐momentum tensor. In the last chapter, the determination of the spinor variables themselves is studied.

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