%0 Generic
%A Petrov, Assen
%D 2008
%F pittphilsci:4089
%K quantum axiomatics, Lie algebras, Hamiltonian theories, spectral duality, invariant cones, equivalent observables, factorization
%T Ten Reasons for Pursuing Multi-Commutative Quantum Theories
%U http://philsci-archive.pitt.edu/4089/
%X Mathematical developments in the 1970s (geometric spectral theory) and 1980s (invariant cones in finite-dimensional Lie algebras) suggest a revision of the standard non-commutative quantum language. Invariantly and covariantly lattice-ordered Lie algebras can replace the known descriptions of the classical and quantum Hamiltonian dynamical systems. The standard operator (or algebraic) quantum theory appears as a factorization of a new multi-commutative model. The multi-commutativity reflects the dependence of the quantum variables on the choice of their measurement procedures--a property required by but not present in the standard quantum theory. The multi-commutativity quantum project needs an advanced theory of invariantly and covariantly ordered infinite dimensional Lie algebras, structures not yet visible on the mathematical agenda.