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University of Nebraska - Lincoln

Quantum Physics

Functional Analysis

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Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert May 2019

Unbounded Derivations Of C*-Algebras And The Heisenberg Commutation Relation, Lara M. Ismert

Dissertations, Theses, and Student Research Papers in Mathematics

This dissertation investigates the properties of unbounded derivations on C*-algebras, namely the density of their analytic vectors and a property we refer to as "kernel stabilization." We focus on a weakly-defined derivation δD which formalizes commutators involving unbounded self-adjoint operators on a Hilbert space. These commutators naturally arise in quantum mechanics, as we briefly describe in the introduction.

A first application of kernel stabilization for δD shows that a large class of abstract derivations on unbounded C*-algebras, defined by O. Bratteli and D. Robinson, also have kernel stabilization. A second application of kernel stabilization provides a ...