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.

20 pages, 16 references; this version contains small corrections with respect to the published one (proposition 8 and proof of theorem 2)

References in corpus (2)

• Mirror particles and mirror matter: 50 years of speculation and search
• On Computational Complexity of Clifford Algebra

Cited by in corpus (2)

• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• On Spinors of Zero Nullity