An Axiomatic Approach to the Formalism of Quantum Mechanics. II.
- 1 June 1966
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 7 (6), 1070-1096
- https://doi.org/10.1063/1.1705000
Abstract
Another axiom has to be introduced to make the formalism given in Part I physically equivalent to the conventional Hilbert‐space formalism. Then it is shown that, given a certain fundamental set of observables, a B*‐algebra can be built into which the set Ob of all bounded observables can be mapped injectively. The closure of the algebra generated by the image of Ob into is itself. A Hilbert space H exists into which the set O0 of all pure physical states can be mapped injectively. The closure of the subset of H which is the image of this mapping is H itself. The algebra can be mapped in such a fashion into the C*‐algebra (H) of all bounded observables that these mappings provide, essentially, just a translation of the original formalism in a Hilbert‐space formalism.
This publication has 2 references indexed in Scilit:
- An Axiomatic Approach to the Formalism of Quantum Mechanics. I.Journal of Mathematical Physics, 1966
- An Algebraic Approach to Quantum Field TheoryJournal of Mathematical Physics, 1964