Is there a Jordan geometry underlying quantum physics?

Wolfgang Bertram (1)

1 IECN - Institut Élie Cartan de Nancy

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of the algebra of observables, in the same way as Lie groups belong to the Lie part. Both the Lie geometry and the Jordan geometry are well-adapted to describe certain features of quantum theory. We concentrate here on the mathematical description of the Jordan geometry and raise some questions concerning possible relations with foundational issues of quantum theory.

Mots clés: generalized projective geometry; Jordan algebra; quantum theory; twistor theory

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Physique Quantique [quant-ph]

Wolfgang Bertram. Is there a Jordan geometry underlying quantum physics?. 2008. ⟨hal-00208072⟩