How Quantum Mechanics Motivates C* Algebras

In this talk we introduce quantum mechanics from first principles. We will illustrate how Stone's theorem and the Stone-von Neumann theorem bridge the gap between the canonical commutation relations for unbounded operators and the Weyl relations for unitary groups. Time permitting, we'll recast the Stone- von Neumann theorem in terms of C* crossed products, and discuss how this motivates natural generalizations of the Stone-von Neumann theorem.