A Tour through Non-Associative Geometry
Abstract
Description
We develop a mathematical concept towards gauge field theories based upon a Hilbert space endowed with a representation of a skew-adjoint Lie algebra and an action of a generalized Dirac operator. This concept shares common features with the non-commutative geometry a la Connes/Lott, differs from that, however, by the implementation of skew-adjoint Lie algebras instead of unital associative *-algebras. We present the physical motivation for our approach and sketch its mathematical strategy. Moreover, we comment on the application of our method to the standard model and the flipped SU(5) x U(1)-grand unification model.
23 pages, LaTeX2e + AMS macros; revised version: This version is consistent with a revision of the application to a GUT in hep-th/9607237
23 pages, LaTeX2e + AMS macros; revised version: This version is consistent with a revision of the application to a GUT in hep-th/9607237