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A geometrical proof of a theorem on spinors. (English) Zbl 0063.06398

From the introduction: B. L. van der Waerden [Gött. Nachr. 1929, 100–109 (1929; JFM 55.0511.09)] and G. E. Uhlenbeck and O. Laporte [Phys. Rev. (2) 39, 1380–1387 (1931; Zbl 0002.09001 and JFM 57.1216.01] have shown that to every skew symmetric self-dual tensor of rank 2 corresponds a symmetric spinor of rank 2. E. T. Whittaker [Proc. R. Soc. Lond., Ser. A 158, 38–46 (1937; Zbl 0016.07901 and JFM 63.1266.02)] has shown that if the above tensor is a null tensor, it corresponds to a spinor of rank 1. The object of this note is to give a geometric proof of the above results.

MSC:

15A66 Clifford algebras, spinors
53B50 Applications of local differential geometry to the sciences
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References:

[1] Van der Waerden :Gottinger Nachrichten, 1929, p. 100; Uhlenbleck and Laporte,Physical Review, Vol. 39, pp. 1380–87. In the above articles, we have a good introduction to the theory of spinors.
[2] E. T. Whittaker : ”On the relations of the tensor calculus to spinor calculus,”Proc. Royal Soc, 1937, Vol. 158. · Zbl 0016.07901
[3] See Uhlenbleck,loc. cit.
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