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arXiv · 1208.0881

On Spinors and Null Vectors

Marco Budinich
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Abstract

We investigate the relations between spinors and null vectors in Clifford algebra with particular emphasis on the conditions that a spinor must satisfy to be simple (also: pure). In particular we prove: i) a new property for null vectors: each of them bisects spinor space into two parts of equal size; ii) that simple spinors form one-dimensional subspaces of spinor space; iii) a necessary and sufficient condition for a spinor to be simple that generalizes a theorem of Cartan and Chevalley that appears now as a corollary of this result. We also show how to write down easily the most general spinor with a given associated totally null plane.

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Marco Budinich. 2012-08-04. On Spinors and Null Vectors. https://doi.org/10.1088/1751-8113/47/11/115201

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