Nonlinear Conformal Transformations and Clifford Algebras

摘要

It is well-known that the conformal group of the real orthogonal space of signature (p,q) with p+q > 2 is doubly covered by the orthogonal group O(p+1,q+1). The nonlinear conformal transformations may be linearized by embedding the compactified orthogonal space of signature (p,q) homogeneously in the orthogonal space of signature (p+1,q+1). Regarding the nonlinear conformal transformations themselves, there is a striking lack of general formulations in the strayed literature. The aim of the paper is to determine the generalization of the familiar (anti-)homographies of the compactified complex plane. The generalization emerges when a very special spinor representation of O(p+1,q+1) (2X2-matrices) is used for the conformal group. (Copyright (c) 1986 by Faculty of Mathematics and Informatics, Delft, The Netherlands.)