Spinor Types in Infinite Dimensions

E. Galina, A. Kaplan, and L. Saal

Abstract: The Cartan - Dirac classification of spinors into types is generalized to infinite dimensions. The main conclusion is that, in the statistical interpretation where such spinors are functions on $\Bbb Z_2^\infty$, any real or quaternionic structure involves switching zeroes and ones. There results a maze of equivalence classes of each type. Some examples are shown in $L^2({\Bbb T)}$. The classification of spinors leads to a parametrization of certain non-associative algebras introduced speculatively by Kaplansky.

Keywords: Spinors, Representations of the CAR, Division Algebras

Classification (MSC2000): Primary: 81R10; Secondary: 15A66

Full text of the article: (for faster download, first choose a mirror)

• Compressed PostScript file (152 kilobytes)
• PDF file (312 kilobytes)