Research Group:

## Algebraic Methods for Quantum Theories

**Topics:**

- introduction to the theory of C*-algebras and von Neumann algebras

- representations

- automorphisms and dynamical systems

- KMS condition

- contraction semigroups

- algebraic formulation of Quantum Mechanics and Statistical Mechanics

- elements on the algebraic and the constructive Quantum Field Theory

## FIR consolidator grant "Cond-Math: Condensed Matter in Mathematical Physics"

**Research topics: **many-body quantum systems, Schrödinger operators, Bose-Einstein condensation, non-linear Schrödinger equations, variational methods in mathematical physics, singular perturbations of Schrödinger operators

## Quantum Mechanics

- scratch course of spectral theory of operators on Hilbert spaces
- a reminder of classical probability
- fundamental postulates of quantum physics
- Heisenberg uncertainty principle
- the von Neumann-Lüders postulate, and the issue of individual states
- symmetries and the Wigner-Kadison theorem
- symmetry groups
- projective representations
- eliminability of multipliers for one parameter groups
- Weyl relations
- von Neumann uniqueness
- CCR and uncertainties