Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics
Mathematical Physics
2011-11-01 v1 math.MP
Quantum Physics
Abstract
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.
Keywords
Cite
@article{arxiv.1110.6607,
title = {Symmetry, Self-Duality and the Jordan Structure of Quantum Mechanics},
author = {Alexander Wilce},
journal= {arXiv preprint arXiv:1110.6607},
year = {2011}
}