On Spinors and Null Vectors
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.
Cite
@article{arxiv.1208.0881,
title = {On Spinors and Null Vectors},
author = {Marco Budinich},
journal= {arXiv preprint arXiv:1208.0881},
year = {2014}
}
Comments
20 pages, 16 references; this version contains small corrections with respect to the published one (proposition 8 and proof of theorem 2)