This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.

We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C-potential function. This result is an extension of [1].

— We study a semi-classical limit of the lowest eigenvalue of a Schrödinger operator on a Wiener space. The Schrödinger operator is a perturbation of the second quantization operator of an unbounded self-adjoint operator by a C3-potential function. This result is an extension of [1].

We continue here the analysis of the previous paper of the Wheeler-DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canonical vacuum quantum gravity in the continuum. In this paper we derive the complete kernel, as well as a physical inner product on it, for a non-symmetric version of the Wheeler-DeWitt operator. We then define a symmetric version of the Wheeler-De...

We consider a positive self-adjoint operator A and formal rank one pertubrations