1208.0881 (Marco Budinich)

On Spinors and Null Vectors    [PDF]

Marco Budinich

We investigate the relations between null vectors and spinors in Clifford algebra with particular emphasis on the conditions that a spinor must satisfy to be simple (also: pure). In particular we show: i) that each null vector bisects the spinor space; ii) that simple spinors are 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 that the most general spinor with a given associated totally null plane can be written immediately without the need to satisfy any of the so called "constraint relations".

View original: http://arxiv.org/abs/1208.0881