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EnglishWe 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.
| Titolo: | On Spinors and Null Vectors |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11368/2722493 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1088/1751-8113/47/11/115201 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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