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Rotation Eigenvectors and Spin 1/2

Richard Shurtleff
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Abstract

It is an easily deduced fact that any four-component spin 1/2 state for a massive particle is a linear combination of pairs of two-component simultaneous rotation eigenstates, where `simultaneous' means the eigenspinors of a given pair share the same eigenvalue. The new work here constructs the reverse: Given pairs of simultaneous rotation eigenvectors, the properties of these pairs contains relationships that are equivalent to spin 1/2 single particle equations. Thus the needed aspects of space-time symmetry can be produced as special cases of more general properties already present in the rotation group. The exercise exploits the flexibility of the rotation group in three dimensions to deduce relativistic quantities in four dimensions.

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Richard Shurtleff. 1999-03-30. Rotation Eigenvectors and Spin 1/2. https://arxiv.org/abs/quant-ph/9903093

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