| We explore a variety of integrality properties emergent in the study of quantum mechanics and representations of Lie groups. In chapter 2, we describe combinatorial methods for perturbation theory including Feynman diagrams, and introduce an alternative diagrammatic technique. In chapter 3, we discuss more general computations for traces of operators relevant in quantum mechanics, and some integrality results using similar techniques. In chapter 4, we prove existence of a Z-form for the universal enveloping algebra of an affine Kac-Moody algebra, analogous to the construction used for Chevalley groups. |
