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Quantum Ontology in the Light of Gauge Theories

Catren, Gabriel (2011) Quantum Ontology in the Light of Gauge Theories. [Preprint]

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    Abstract

    We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively.


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    Item Type: Preprint
    Keywords: quantum mechanics; gauge theories; geometric quantization; symplectic reduction
    Subjects: Specific Sciences > Physics > Quantum Mechanics
    Specific Sciences > Physics > Symmetries/Invariances
    Depositing User: Dr. Gabriel Catren
    Date Deposited: 04 Feb 2011 11:21
    Last Modified: 04 Feb 2011 11:21
    Item ID: 8478
    URI: http://philsci-archive.pitt.edu/id/eprint/8478

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