Transition amplitude spaces
Stanley Gudder, Sylvia Pulmannová
Motivated by physically plausible axioms, the concept of a transition amplitude space (tas) is defined. Various connections between this framework and other axiomatic approaches to the foundations of quantum mechanics are derived. In particular, transition probability spaces, the algebraic approach, the operational statistics and quantum logic approaches, and traditional Hilbert space quantum mechanics are considered. It is shown that a tas always admits a Hilbert space representation. Results are obtained concerning isomorphisms and automorphisms for tas’s. The concept of an A-form is introduced and the relationship between certain A-forms and bounded linear operators on a Hilbert space are studied. Finally, it is shown that sums and tensor products of tas’s can be formulated in a natural way.
Journal of Mathematical Physics•Feb 1, 1987•10 citations