Quantum theory of measurement based on the many-Hilbert-space approach

Mikio Namiki

Abner Shimony, Howard Stein

John F. Cyranski

It is shown how quantum theory (QT) can be expressed as a probability theory on Hilbert space, treated as a measure space. The approach generalizes the work of Bach and clarifies the ’’generalized trace’’ of Langerholc. It permits the description of both bounded and unbounded observables as measurable functions. Dynamical evolution can be described in terms of stochastic processes.

E. Celeghini

Abstract The Paradigms introduced in philosophy of science one century ago are shown to be quite more satisfactory of that introduced by Galileo. This is particularly evident in the physics based on Hilbert Spaces and related mathematical structures that we apply in this paper to Quantum Mechanics and to Theory of Images. An exhaustive discussion, that include the algebraic analysis of the operators acting on them, exhibits that the Hilbert Spaces-that have fixed dimension-must be generalized to the Rigged Hilbert Spaces that contain spaces with continuous and discrete dimensions. This is the property of Rigged Hilbert Spaces that allows a consistent formal description of the physics we are considering. Theory of Quantum Mechanics and of Images are similar and the fundamental difference between them comes from the definition of measure that is outside the theory of the spaces: while in Quantum Mechanics the measure is a probabilistic action, in Images it is a classical functional.

Masatoshi Namiki, Saverio Pascazio

Jan Peřina, Z. Hradil, Branislav Jurčo