The theory of unbounded derivations in C^* -algebras and its applications to statistical mechanics

这项研究涉及C^*-代数中的无界导子理论，该学科的研究是由量子物理和统计力学推动的。这是一个活跃的研究领域，该理论最雄心勃勃的目标之一是在C^*-理论的框架内发展量子统计力学。结果集中在涉及量子统计力学和流形中的微分学的主题上。其中一个目标是在C^*-集合中以最一般的形式来表示相变的不存在定理。第一次，首席研究者在这一背景下全局地构造了相当广泛的一类相互作用模型的派生，并提出了一种新的辅助处理来构造时间演化和KMS状态。

This research is concerned with the theory of unbounded derivations in C^* -algebras, a subject whose study was motivated by quantum physics and statistical mechanics. This is an active area of research, and one of the most ambitious aims of the theory is to develop quantum statistical mechanics within the framework of the C^* -theory. The results concentrate on topics involving quantum statistical mechanics and differentiation in manifolds. One of the goals is to formulate the absence theorem of phase transitions in the most general form within the C^* -setting. For the first time, the principal investigator globally constructs within that setting, derivations for a fairly wide class of interaction models and present a new aidomatic treatment of the construction of time evolutions and KMS states.