English

The Mathematical Footing of Non-associative Geometry

High Energy Physics - Theory 2008-02-03 v2

Abstract

Starting with a Hilbert space endowed with a representation of a unitary Lie algebra and an action of a generalized Dirac operator, we develop a mathematical concept towards gauge field theories. This concept shares common features with the non--commutative geometry a la Connes/Lott, differs from that, however, by the implementation of unitary Lie algebras instead of associative *-algebras. The general scheme is presented in detail and is applied to functions \otimes matrices.

Keywords

Cite

@article{arxiv.hep-th/9607094,
  title  = {The Mathematical Footing of Non-associative Geometry},
  author = {Raimar Wulkenhaar},
  journal= {arXiv preprint arXiv:hep-th/9607094},
  year   = {2008}
}

Comments

39 pages, LaTeX2e + AMS macros, revised version: modified definition of an ideal, because the old definition leads to a vanishing Higgs potential in the standard model (hep-th/9607096)