A Tour through Non-Associative Geometry

Details A Tour through Non-Associative Geometry A Tour through Non-Associative Geometry

1996-07-11

arxiv.org/abs/hep-th/9607086v2

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, LaTeX2e + AMS macros; revised version: This version is consistent with a revision of the application to a GUT in hep

Scientific paper

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.

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