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Coordinate Formalism on Abstract Hilbert Space: Kinematics of a Quantum Measurement

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Abstract

Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.

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  1. UWC Department of Mathematics, University of Wisconsin, 780 Regent Street, Madison, Wisconsin, 53708

    Alexey A. Kryukov

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  1. Alexey A. Kryukov
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Kryukov, A.A. Coordinate Formalism on Abstract Hilbert Space: Kinematics of a Quantum Measurement. Foundations of Physics 33, 407–443 (2003). https://doi.org/10.1023/A:1023711631257

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  • DOI: https://doi.org/10.1023/A:1023711631257

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