Coordinate Formalism on Abstract Hilbert Space: Kinematics of a Quantum Measurement [Book Review]

Foundations of Physics 33 (3):407-443 (2003)
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
Keywords improper states  generalized eigenvalue problem  quantum measurement
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