On Unitary Positive Energy and KMS Representations of Some Infinite-Dimensional Lie Groups

Abstract

In this dissertation, we study (projective) unitary representations of possibly infinite dimensional locally convex Lie groups, in the sense of Bastiani, that either satisfy a positive energy condition, or a KMS(Kubo-Martin-Schwinger) condition. Both of these are motivated by physics. The main purpose of this thesis is to gain general understanding for these classes of representations, and more specifically to develop general tools by which they can be studied in systematic fashion. These tools are consequently applied to specific cases of interest, demonstrating that these conditions are typically extremely restrictive, that the classification of these classes of representations is feasible in various cases, and that these tools can be effectively applied towards achieving such a classification....