# Mathematical Foundations of Quantum Mechanics: An Advanced Short Course

August 27, 2015

This paper collects and extends the lectures given by the author at the "XXIV
International Fall Workshop on Geometry and Physics" held in Zaragoza (Spain)
during September 2015. Within these lectures I review the formulation of
Quantum Mechanics, and quantum theories in general, from a mathematically
advanced viewpoint, essentially based on the orthomodular lattice of elementary
propositions, discussing some fundamental ideas, mathematical tools and
theorems also related to the representation of physical symmetries. The final
step consists of an elementary introduction the so-called (C*-) algebraic
formulation of quantum theories.

Keywords:

quantum mechanics, spectral theory, von Neumann algebras, superselection rules, group representaton