Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics

Details Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics

2011-10-30

arxiv.org/abs/1110.6607v1

Physics

Mathematical Physics

Scientific paper

I explore several related routes to deriving the Jordan-algebraic structure of finite-dimensional quantum theory from more transparent operational or physical principles, mainly involving ideas about the symmetries of, and the correlations between, probabilistic models. The key tool is the Koecher-Vinberg Theorem, which identifies formally real Jordan algebras with finite-dimensional order-unit spaces having homogeneous, self-dual cones.

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