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A Tour through Non-Associative Geometry

Raimar Wulkenhaar
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Abstract

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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Raimar Wulkenhaar. 1997-02-10. A Tour through Non-Associative Geometry. https://arxiv.org/abs/hep-th/9607086

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