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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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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
Petrov, Assen
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 15:16
Item ID: 4089

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