On a Jordan-algebraic formulation of quantum mechanics: Hilbert space construction
High Energy Physics - Theory
2007-05-23 v1
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 Schr\"odinger equation on this Hilbert space.
Keywords
Cite
@article{arxiv.hep-th/9304124,
title = {On a Jordan-algebraic formulation of quantum mechanics: Hilbert space construction},
author = {Wolfgang Bischoff},
journal= {arXiv preprint arXiv:hep-th/9304124},
year = {2007}
}
Comments
12pages, latex, THEP 93/7