The method of moments and nested Hilbert spaces in quantum mechanics

Dave Applebaum

D�nes Petz

A. Großmann

A nested Hilbert space is a pair of Hilbert spaces H0, H1, each of which is in a certain sense identified with a dense subset of the other. These structures are used here to study analytic continuation into ``unphysical sheets'' and to discuss nonnormalizable states of quantum-mechanical systems.

Sujeewa Wickramasekara, Arno Böhm

We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous representations in a nested scale of Hilbert spaces. We also construct a couple of examples illustrative of the key features of group representations in rigged Hilbert spaces. Finally, we establish a simple criterion for the integrability of an operator Lie algebra in a rigged Hilbert space.

Martin Bojowald, Suddhasattwa Brahma, Umut Büyükçam +1 more

A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and semiclassical equations, based on general properties of quantum moments.