Spinors, Pseudo-Quaternions, and Orthogonal Groups

Abstract

By using explicit forms for the Clifford matrices in V^s a subsystem {Q_u } of the Clifford algebra is devised which is an orthogonal (rotation) group, i.e. QQT = 1, det Q = + 1. The matrices Q_u (" pseudo-quaternions ") are in (1, 1) correspondence with vectors u of Vs which satisfy a certain quadratic condition (" spinors " ) , and in (2, 1) correspondence with the full rotation group of matrices A in V _{4 The matrices A are given explicitly in terms of quadratic forms of spinors.}