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Ten Reasons for Pursuing Multi-Commutative Quantum Theories

Petrov, Assen (2008) Ten Reasons for Pursuing Multi-Commutative Quantum Theories. [Preprint]

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    Abstract

    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.


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    Item Type: Preprint
    Keywords: quantum axiomatics, Lie algebras, Hamiltonian theories, spectral duality, invariant cones, equivalent observables, factorization
    Subjects: Specific Sciences > Mathematics
    Specific Sciences > Physics > Quantum Mechanics
    General Issues > Science Policy
    Depositing User: Assen Petrov
    Date Deposited: 29 Jun 2008
    Last Modified: 07 Oct 2010 11:16
    Item ID: 4089
    URI: http://philsci-archive.pitt.edu/id/eprint/4089

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