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On a Jordan-algebraic formulation of quantum mechanics: Hilbert space construction

Wolfgang Bischoff
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Abstract

In this note I discuss some aspects of a formulation of quantum mechanics based entirely on the Jordan algebra of observables. After reviewing some facts of the formulation in the \CS -approach I present a Jordan-algebraic Hilbert space construction (inspired by the usual GNS-construction), thereby obtaining a real Hilbert space and a (Jordan-) representation of the algebra of observables on this space. Taking the usual case as a guideline I subsequently derive a Schrödinger equation on this Hilbert space.

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Wolfgang Bischoff. 1993-04-26. On a Jordan-algebraic formulation of quantum mechanics: Hilbert space construction. https://arxiv.org/abs/hep-th/9304124

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