We investigate the relations between spinors and null vectors in Clifford algebra of any dimension with particular emphasis on the con- ditions that a spinor must satisfy to be simple (also: pure). In partic- ular we prove: i) a new property for null vectors: each of them bisects spinor space into two subspaces 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 which becomes a corollary of this result. We also show how to write down easily the most general spinor with a given associated totally null plane.

On Spinors and Null Vectors

BUDINICH, MARCO
2014-01-01

Abstract

We investigate the relations between spinors and null vectors in Clifford algebra of any dimension with particular emphasis on the con- ditions that a spinor must satisfy to be simple (also: pure). In partic- ular we prove: i) a new property for null vectors: each of them bisects spinor space into two subspaces 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 which becomes 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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11368/2722493
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