On spinors in n dimensions

Abstract

The matrix which enters in the charge conjugation transformation of the usual spinors in 4-space is an invariant matrix and is skew symmetric. It is shown that there exists such an invariant matrix C for any number of dimensions (and independent of the number of time like dimensions). Its symmetry properties depend on tile dimension number n modulo 8. With the help of the C matrix one can construct, for n = 1, 2, 7, 8 mod 8, an n-dimensional invariant bilinear in the components of a single n-dimensional spinor. Some examples are given for n = 2, 3, 7. A bilinear baryon invariant is formed for a theory with high symmetry. Its existence is closely related to the triality property of 8-space.