Differential calculus on Jordan algebra and Jordan modules
Alessandro Carotenuto, Ludwik Dabrowski, Michel Dubois-Violette
TL;DR
This paper develops differential calculus and connection theory on Jordan algebras, especially the exceptional Jordan algebra, with potential applications in particle physics.
Contribution
It introduces a comprehensive framework for differential calculus and connections on Jordan modules, including the exceptional case, advancing mathematical tools for physics applications.
Findings
Complete characterization of connections on free Jordan modules.
Development of differential calculus over the exceptional Jordan algebra.
Framework applicable to particle physics models.
Abstract
Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on differential calculus over the exceptional Jordan algebra and provide a complete characterization of the theory of connections for free Jordan modules.
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