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arXiv · hep-th/9310148

Algebraic connections on parallel universes

R. Coquereaux·R. Haussling·F. Scheck
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Abstract

For any manifold $M$, we introduce a $\ZZ $-graded differential algebra $Ξ$, 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 $Ξ$ does not rely on a given Dirac-Yukawa operator acting on a space of spinors.

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R. Coquereaux, R. Haussling, F. Scheck. 1993-10-22. Algebraic connections on parallel universes. https://doi.org/10.1142/s0217751x95000048

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