Algebraic connections on parallel universes

Details Algebraic connections on parallel universes Algebraic connections on parallel universes

1993-10-22

arxiv.org/abs/hep-th/9310148v1

Int.J.Mod.Phys. A10 (1995) 89-98

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, CPT-93/PE 2947

Scientific paper

10.1142/S0217751X95000048

For any manifold $M$, we introduce a $\ZZ $-graded differential algebra $\Xi$, which, in particular, is a bi-module over the associative algebra $C(M\cup M)$. We then introduce the corresponding covariant differentials and show how this construction can be interpreted in terms of Yang-Mills and Higgs fields. This is a particular example of noncommutative geometry. It differs from the prescription of Connes in the following way: The definition of $\Xi$ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.

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