The Jordan formulation of Quantum Mechanics: a review

This is a transcription of a conference proceedings from 1985. It reviews the Jordan algebra formulation of quantum mechanics. A possible novelty is the discussion of time evolution; the associator takes over the role of $i$ times the commutator in the standard density matrix formulation, and for the Jordan algebra of complex Hermitian matrices this implies a Hamiltonian of the form $H= i[x,y] + \lambda \mathbb{I}$ for traceless Hermitian $x,y$ and real number $\lambda$. Other possibilities for time evolution in the Jordan formulation are briefly considered.